4

1 Jsl #lalij Ouslas)1. Jlgwll (4 Points) Letyl(r) be the solutionfor the DE: ydx = W} xyldy If yle) = I then at $ = the value of y will satisfyY = 2O e =-0Y=-Je=-1J...

Question

1 Jsl #lalij Ouslas)1. Jlgwll (4 Points) Letyl(r) be the solutionfor the DE: ydx = W} xyldy If yle) = I then at $ = the value of y will satisfyY = 2O e =-0Y=-Je=-1Ja =2

1 Jsl #lalij Ouslas) 1. Jlgwll (4 Points) Letyl(r) be the solutionfor the DE: ydx = W} xyldy If yle) = I then at $ = the value of y will satisfy Y = 2 O e =-0 Y=- Je=-1 Ja =2



Answers

1. $$y^{\prime \prime}-2 y^{\prime}+y=g(t) ; \quad y(0)=-1, \quad y^{\prime}(0)=1$$

We have the equation X y plus y squared equals one Trying to find the value of the second derivative. I'm using the prime notation at the 0.0 negative one. So it started about finding the first your evidence using the chain rule. It would be x times the derivative of why, with respect X y crime. Plus why times the derivative of X which is just one then then plus derivative of y squared would be too. Why times y prime that equals zero derivative of a constant. It's always zero. Now let's solve this for y prime. So we will factor the UAE prime out of those two terms. So we've got X Plus two y kind of like prime and move the by over to the other side's that we call negative why? And then we divide both sides to get why prime by itself. So why prime equals negative? Why over X plus two y. Now I can find my second derivative by taking the derivative of that equation. So why Double prime is gonna equal bottom function X plus two y times the derivative of the top, which is gonna be negative y prime minus the top function Negative. Why times the derivative of the bottom, which will be one plus two. Why prime? That's all divided by the denominator X plus two y square to a little bit nicer. There we go. Now we want to evaluate this at the 0.0 negative one. Which means because we have why primes in this. We also have to evaluate that at the 0.0 negative one. So why prime evaluate that zero negative one is going to be negative of negative one over zero plus two times negative one that's gonna end up giving us negative 1/2. Now we can substitute into our wide double prime. And I'm gonna clean up the algebra little bit as I do that as well. So why Double Prime evaluated it? Zero negative one. We have X, which is zero plus two times negative one. So let's just make that a minus two times the negative. Why Prime are negative 1/2 and then the minus and the negative. I'm just gonna make that a plus factor. Let's just leave it minus because the negative of why have become a positive one times one plus two times y prying the negative 1/2. And that holds getting divided by zero plus two times negative 1/2 being square. Okay, well, the two negatives here become positive. So negative. Two times 1/2 will give us a negative one. The two times the negative 1/2 will give us negative one plus 10 So that would just be minus zero. Up in the top. Divided by that would be negative. One being squared. Negative one squared is one. So we should have a final answer. Uh, negative one for our second driven.

But the we're trying to find the second derivative evaluated at zero negative one. I'm used gonna be using my prime notation here instead of the to buy over DX to notation so doing implicit differentiation. Here we've got first function times the derivative of the second derivative lives. Why Prime lost the second function? Why? Times The driven of the first derivative of X is just one than plus the driven about why square will be to why his wife prime not a equal derivative of a constant is zero. No, I need to get the white crimes by themselves. So it's combined those two terms together in fact, at the wide prime. So X plus two y times y prime will stay on the left hand side. Now let's move this. Why here, Over to the other side's other equal. Negative Why? And that means that, like prime is gonna equal negative. Why over next plus two I So there's our first derivative. Now we need second derivative. So why double primal equals the derivative up this fracture So using the quotient rule bottom exposed to lie times the derivative of the top negative prime minus the top negative. Why Times the derivative of the bottom derivative of X is one and the derivative of two. Why will be plus two? Why prime and then all gets divided by the denominator X plus two I being squared. So now we have to evaluate it at our 0.0 negative one. And we also have y prime in this equation. So that means we also have to revaluate. Why prime at the 0.0 negative one so that we know that value. So that would give us negative of a negative one over zero plus two times negative one that's gonna end up giving us negative 1/2. So that means that why double prime evaluated at Lu zero negative one well equal X, which is zero plus two times the negative one times the negative of our UAE prime. So I'll just be positive 1/2 and then minus the negative of why on negative negative one is one times one plus two times are white prime negative 1/2 and that all gets divided by zero cost two times negative, one being squared. So we have negative two times 1/2 a lot of the negative one And then that's also a negative 12 times negative. 1/2 plus the born is going to get a zero. So I don't have to subject anything there that's gonna get divided by negative two squared, negative to square. It is for so our second derivative at the 0.0 negative one equals.

Okay, so here were considered, with each being equal 0.25 on the interval of zero and one we're gonna evaluate at a 0.25 quit five 0.75 Oh, and one. Okay, But before we do that, we're gonna start by rewriting our equation that were given. So the second derivative is on its own, and that that is equal to 1/1 plus t squared times. Why? Minus one over one plus t square times. Why, prime? So make our so institutions as we've been doing where we set x one equal toe Y and X two equal to y prime, which, of course, is the same as, uh, X one prime. So that changes our system. And that will change it to x one prime being equal to x two and x two Prime be equal to 1/1 plus t squared times x one minus 1/1 plus t square times x two. Okay. And so then the initial values are I'm gonna have X one of zero, which is equal to R Y. Zero right is equal to one. Represent that his little X one, comma zero and we have our x two, the zero which is really our Why prime that were given people the negative one. Well, let that be X to come A zero. So now we can apply oilers method. And so just a reminder. Oilers method is X and plus one is equal Thio accident plus each then the function t n xn. So Step one and we have t one would be equal to t not plus h s is gonna be equal to zero plus 0.25 is equal to 0.25 right? And so, you know, we started talked about this is the very beginning as to where we were going to be, which values we would be doing our calculations on. Okay, so step two. Yeah, I suppose I should finish step one first. So that means when you take x one at 0.25 which would be approximately equal to x 11 which is equal thio x 10 plus each times x 20 So that's gonna be equal to next of one musical one. Plus, we'll have 80.25 Next to zero was negative. One eso This is 0.75 Yes, and we have that X two at 0.25 is approximately equal to x 21 which is equal to H times. Okay, one over. Mhm one plus teaser square times X some 10 minus 1/1, plus Kina square times x up to zero. Que looks pretty complicated, but we have all these values. Um and we calculated, of course, I miss one little piece here, So plus T x 20 Right, So this ends up being a 0.25 times one plus one minus one, which is equal to negative 0.5. So Step two. Here we get t two, which would be equal to t one plus 10.5. So that's 0.25 plus 0.25 is equal 2.5. So we are worried about x one and 0.5, which is a proximate to x 12 which is equal to x 11 plus h times x +21 which is equal to 0.75 plus 0.25 times negative. 0.5 that is equal to 0.6 to 5. It's mostly a lot of, um, plugging these numbers in the next two at 0.5 is gonna be roughly equal to x 22 So that is Follow the pattern next to one plus each. Times one over one plus t one squared times x 11 minus 1/1 plus t one square next to one. This simplifies to negative 0.5 plus 0.25 I'm just gonna pull this, um, fraction that we see repeating out, So I want to write it twice. Should be won over one plus 0.25 squared times 0.75 plus 0.5. According to the calculator, that is negative 0.20 six. Roughly depending on where you want Thio. Stop. I suppose a few minutes from places won't hurts. Will say 20588 Okay, we have two more of these to do. Step three. Okay, So, t three, I'm just gonna add 0.25 so it's gonna be equal toe 0.75 So we want x one at 10.75 Sequel approximately equal to x 13 which is equal to x 12 plus each x to to. Okay, so that is 0.6 to 5 plus zero point 25 times negative 0.20588 And that is 0.57353 Then the more complicated version next 2.75 is roughly equal to next to three, which is equal to x 22 plus each. Times 1.1 plus t two squared times x 12 minus 1/1 plus t squared x 22 Okay. And so we just plug these numbers and again. So this time we have a negative point to 0588 plus 0.2 5/1 plus 0.5 squared times 0.6 to 5 minus. There's gonna be plus with a minus negative. 0.20588 Okay. And the calculator says this is negative. 0.39 704 Finally, our last step here t four will be equal to one. It's 10.75 plus 0.25 So we want X one at one, which is approximately X one four is equal to x one three plus each times x 23 okay. And So that is 0.5 73 53 plus 0.25 times this negative zero point 039 704 And that is equal to 0.5 six 3604 Okay, the next two of one is approximately equal to x two four, just equal to x 23 plus h times. Let's say 1/1 plus t three squared times X one three minus x 23 I just figure out this, um, to save writing a little bit, so enjoy, right that fraction twice. But this ends up being equal to negative 0.0 39704 plus 0.2. That's a strange looking to since your 0.25 r h And then So now I'm combining this h with this fractions that B one plus 10.75 squared. And then we take the values from our previous around here, which is your 0.5 seven 353 plus zero point 039 70 four really made it. Okay. And today is a good day to love your calculator. Uh, 0.0 58 413 And so that's gonna be the last calculation. And I suppose we could have skipped that step, but we didn't. So, um, since why is equal to x one? Our approximations that we get is that why 0.25 is equal to 0.75 That why a 0.5? It is equal to zero point six 25 You have Y of 0.75 and that waas zero point 573 53 And lastly, our why of one is zero point 56 36 03


Similar Solved Questions

5 answers
3 ? 4-0v] o42 +7 - = (41^ smh~w mias 0 ma 48 [JNF ^p
3 ? 4-0v] o42 +7 - = (41^ smh ~w mias 0 ma 48 [JNF ^p...
5 answers
Problem 19. Use the quark triplet diagramto construct the baryon decuplet that includes the following members: qqq BaryonLlL uud udd ddd LuS uds dds2 : 0 ~8 uSS dss -1 -2 SSS ~1X*+ X*0 C* Z*0 2 5
Problem 19. Use the quark triplet diagram to construct the baryon decuplet that includes the following members: qqq Baryon LlL uud udd ddd LuS uds dds 2 : 0 ~8 uSS dss -1 -2 SSS ~1 X*+ X*0 C* Z*0 2 5...
5 answers
Question 4 Not yet answered Marked out of 1.00Flag questionFrom 'normally dktrbute n population random sample of slze chosen YIth varlance 9598 forthe populauon vanianceAl (33.64, 166.10) (34.71,168.451 C) (30.23,164.521 DI (31.53,155,72| El (32.58.160.91)Select one:
Question 4 Not yet answered Marked out of 1.00 Flag question From 'normally dktrbute n population random sample of slze chosen YIth varlance 9598 forthe populauon vaniance Al (33.64, 166.10) (34.71,168.451 C) (30.23,164.521 DI (31.53,155,72| El (32.58.160.91) Select one:...
5 answers
Suppose S00. mL flask flled with L.1 mol of CO, 2.0 mol of NO &nd 0.60 mol ot COz: The felloalng NOz(g)+cOlg) ~ No(g)+COz()The equlllbrium constant K for this reaction 0.634 at the temperature of the flask:Calculate the equilibrium molarlty of CO. Round your answer two declmal places.
Suppose S00. mL flask flled with L.1 mol of CO, 2.0 mol of NO &nd 0.60 mol ot COz: The felloalng NOz(g)+cOlg) ~ No(g)+COz() The equlllbrium constant K for this reaction 0.634 at the temperature of the flask: Calculate the equilibrium molarlty of CO. Round your answer two declmal places....
5 answers
Trut Or_falll? Ktrvli Soy why ie faSet provide [bunferexampLe Tesavrne W atetan n Sn Lenverde
trut Or_falll? Ktrvli Soy why ie faSet provide [bunferexampLe Tesavrne W atetan n Sn Lenverde...
1 answers
Which of the following reactions will give acetophenone as a product? (a) Acid catalysed hydration of styrene followed by oxidation with hot alkaline $\mathrm{KMnO}_{4}$. (b) Phenyl acetylene $\stackrel{\mathrm{d} \mathrm{H}, \mathrm{SO}_{4}^{\prime} \mathrm{H}_{\mathrm{E}}^{2+}}{\longrightarrow}$ Aldehydes, Ketones and Carboxylic Acids (c) Reaction of benzoyl chloride with dimethyl cadmium. (d) Dry distillation of a mixture of calcium acetate and calcium benzoate.
Which of the following reactions will give acetophenone as a product? (a) Acid catalysed hydration of styrene followed by oxidation with hot alkaline $\mathrm{KMnO}_{4}$. (b) Phenyl acetylene $\stackrel{\mathrm{d} \mathrm{H}, \mathrm{SO}_{4}^{\prime} \mathrm{H}_{\mathrm{E}}^{2+}}{\longrightarrow}$ A...
5 answers
In the Periodic Table below, shade all the elements for which the neutra? atom has partially-filled p subshell:MnMolMg
In the Periodic Table below, shade all the elements for which the neutra? atom has partially-filled p subshell: Mn Mol Mg...
5 answers
Write the mechanism for the base-catalyzed formation of a cyclic $eta$ -keto ester from a 1,7-diester.
Write the mechanism for the base-catalyzed formation of a cyclic $\beta$ -keto ester from a 1,7-diester....
5 answers
Find difference in brightness of Sirius and Arcturus Sirius and Vega and Arcturus and VegaAccording to stellarium-web org:Sirius BrightnessArcturus Brightness is: 0.11_Vega Brightness is: .09_Difference in brightness of Sirius and Arcturus is:Sirius is _1 09and Arcturus is 011Difference in brightness of Sirius and Vega is:Siriusis _L0Qand Vegais 0.09Difference in brightness of Arcturus and vegaArcturus is 01Land Vega is 009
Find difference in brightness of Sirius and Arcturus Sirius and Vega and Arcturus and Vega According to stellarium-web org: Sirius Brightness Arcturus Brightness is: 0.11_ Vega Brightness is: .09_ Difference in brightness of Sirius and Arcturus is: Sirius is _1 09and Arcturus is 011 Difference in br...
1 answers
In Exercises 9–14, determine the order of the matrix. $$\left[\begin{array}{rrrr}{-3} & {7} & {15} & {0} \\ {0} & {0} & {3} & {3} \\ {1} & {1} & {6} & {7}\end{array}\right]$$
In Exercises 9–14, determine the order of the matrix. $$\left[\begin{array}{rrrr}{-3} & {7} & {15} & {0} \\ {0} & {0} & {3} & {3} \\ {1} & {1} & {6} & {7}\end{array}\right]$$...
5 answers
Prove that if f(2) is holomorphic in a domain 0, then its real and imaginary parts are harmonic finctions in 02.
Prove that if f(2) is holomorphic in a domain 0, then its real and imaginary parts are harmonic finctions in 02....
5 answers
Saunpnns uaamloq diysuoneizi EpilaupoauaisJe4mJNI PuE sajnpnjis ujamlaq diysuoneqa) [e>iwaupoajais Ju Jeum (pue [ sJJMns uajknao djysuonejau |83jualpoaja1s J11 51 Je4M (8 {(eJQuapi 'SJQlOaJJISCip "sjawoqlueua 2)M sainnnns ujordao diysuoneja IeoiuJudoiaic Jr4M (YHO ZHN_ 3hEHo_Eho_JhEho-ZHN Jh Eho NZH HO (III HOEhj NZH +HO(l(ype3 sd Z) mojaq UMOUS suopalojd uruumat 341 UO paseq suonsanb Bumolloj 341 JaMSue aseoidNOILsJnO'smejs uopjaiduoj uopisar
saunpnns uaamloq diysuoneizi Epilaupoauais Je4m JNI PuE sajnpnjis ujamlaq diysuoneqa) [e>iwaupoajais Ju Jeum ( pue [ sJJMns uajknao djysuonejau |83jualpoaja1s J11 51 Je4M (8 {(eJQuapi 'SJQlOaJJISCip "sjawoqlueua 2)M sainnnns ujordao diysuoneja IeoiuJudoiaic Jr4M (Y HO ZHN_ 3h EHo_ Eho_...
5 answers
000 1 W 1 1HL 1 W L 1
000 1 W 1 1 HL 1 W L 1...
5 answers
The performance 0i Creative Ideas was poOr Whal poor? (Round your answer t0 decimal places:}probablllty that the performance of the world economy had also beer
The performance 0i Creative Ideas was poOr Whal poor? (Round your answer t0 decimal places:} probablllty that the performance of the world economy had also beer...

-- 0.021577--