5

Solve the initial-value problem shown below: dy dc =I V1-v? y (0) = 0 Give an exact formula for ysin (a)3sin3...

Question

Solve the initial-value problem shown below: dy dc =I V1-v? y (0) = 0 Give an exact formula for ysin (a)3sin3

Solve the initial-value problem shown below: dy dc =I V1-v? y (0) = 0 Give an exact formula for y sin (a) 3 sin 3



Answers

Solve the given differential equation by separation of variables. $$\sin 3 x d x+2 y \cos ^{3} 3 x d y=0$$

16 dot to problem number three were dealing with linear, ordinary first order differential equations. So in order to do this, we need to get this in standard forms. A standard form is going to be why prime plus some function of X times Why is equal to some function of X? If we can get the different equation in this form, then my integrating factor multiply the entire equation by e to the integral Peter DX DX that will allow me to solve this different you equation. So standard form. Why prime plus three over X Y is equal to sign X over execute. So this is where I will go to find my integrating factor. So I need to figure out what is e to the three over X t X. So that's just going to be easy to the three natural log Absolute value of X. We know that X is positive. So this is going to be e to the three natural log of X, which is e to the natural log of X cubed, which is X cubed. So the entire equation gets multiplied by execute. So why prime plus three over x one equal sign of X over X cubed. Make this a little bit clear for multiply this and type equation by X cubed And so what you're gonna have on the left side, you're gonna have X cubed. Why the derivative with respect to X? So that's just the product rule. Because if you differentiated this, um, you would have X cubed times y prime, which is what you have there. And then you would also have three X squared times. Why, so anyway, this is allows us to solve this equation. What I have on the right side of equation is just a sign of X. So now I integrate both sides of this equation, and I have execute why is equal to minus co sign of X plus a constant. So that tells us that why is equal to you Just divide everything by X cubed so minus the coastline of X rex cubed plus see over execute. And so that is my final solution

More we want to find the differential do I? For why is equal to arc sine execute? We're going to rely on differentiation shortcuts to find dy dx and then we'll find do I by multiplying both sides by the X to do so? We're going to use our differentiation shortcuts that I just mentioned in particular the inverse trig derivatives that we've recently learned. So I have the three major investment resistance here were primarily going to use dB X, X and X equals 1/1 minus X squared because arcs annexes cube. We're also going to use the chain with salt so we can proceed to solve it now why is already in its most easily defensible form that we derive as follows. Do I D X is equal to three arc sine X squared times rid of what's inside parentheses, which is 1/1 minus x squared square rooted. Thus we can push the X to the right hand side. And we have our differential solution that is do I. Is equal to three arc sine X squared all over route women, it's X squared dx

This question asks is to solve the given differential equation. The first step would be two Take the integral of each separate terms. So why do you why, plus the integral of sine of why do you? Why is equivalent to the integral of axe de ax plus the integral of X cubed de axe? So the integral of why do you why we increase the expert by one divide by the new exponents And then we have negative coast Sign of why And then we increased the expert by one divided by the new exponents and they do it again increased the expert from 3 to 4. This simplifies to why squared is too co sign of why plus X squared plus X to the fourth over to and then plus C o k. That's

Later. One. Today we're going to solve a problem. Number 17 here. What you could do. Three x minus Science square. It's divided by the X He called toe three minus to sign X Koszics diva Equal toe three minus two. Say next because it's in new DX. Thank you.


Similar Solved Questions

5 answers
2)(a Show that4 pin K-2converges
2) (a Show that 4 pin K-2 converges...
5 answers
25. Name each compound. [(CH3 JNH] +NO;-[(CH;CH2)NHz] +CI
25. Name each compound. [(CH3 JNH] +NO;- [(CH;CH2)NHz] +CI...
5 answers
What state of chromatin can increase the occurrence of cell division? loosety compacted histones near oncogenes loosely compacted hustones nejr apoptot Eenes loosely compacted histoncs neur umar suppressor Benes loosely compacted nstones ncar DNA (ransocjses all ef these options plausiblaMovrg anotnef question Wil savt Ihls rCsDonst( ; .
What state of chromatin can increase the occurrence of cell division? loosety compacted histones near oncogenes loosely compacted hustones nejr apoptot Eenes loosely compacted histoncs neur umar suppressor Benes loosely compacted nstones ncar DNA (ransocjses all ef these options plausibla Movrg anot...
5 answers
If it does, find all possible values of c in (-1, 2) satisfying the conclusion of the MVT:13 C = 12. C = ~13. C = 01 2 1 24. C =5. C =6 hypotheses not satisfied7 . C =2
If it does, find all possible values of c in (-1, 2) satisfying the conclusion of the MVT: 13 C = 1 2. C = ~1 3. C = 0 1 2 1 2 4. C = 5. C = 6 hypotheses not satisfied 7 . C = 2...
5 answers
Show the products obtained from addition of methylmagnesium bromide to the following compounds:(a) Cyelopentanone(b) Benzophenone (diphenyl ketone)(c) 3-Hexanone
Show the products obtained from addition of methylmagnesium bromide to the following compounds: (a) Cyelopentanone (b) Benzophenone (diphenyl ketone) (c) 3-Hexanone...
5 answers
67.54SI-EOT-MATOTRadic eualtonsWhich ofthe following Is/are the solution(s) of the equation 2 =-r+Vzr+3 Hunt: Check solutons for possible extranenus solutions1=onlyonlyBoth X= 2 und4F 2 Oly
67.54 SI-EOT-MATOT Radic eualtons Which ofthe following Is/are the solution(s) of the equation 2 =-r+Vzr+3 Hunt: Check solutons for possible extranenus solutions 1= only only Both X= 2 und 4F 2 Oly...
5 answers
Pi GIVEN: A {Pi. pz pa} c Pz where Pz P p = 2 -3x+ Sr? FIND: [p]1+x? -X 1 - 2xNOTE: A is an ordered basis
Pi GIVEN: A {Pi. pz pa} c Pz where Pz P p = 2 -3x+ Sr? FIND: [p] 1+x? -X 1 - 2x NOTE: A is an ordered basis...
5 answers
A solution is prepared by dissolving 171 g of CdCl2 in water to form 250.0 mL of solution. If the density of the solution is 1.556 g / mL, what is the molarity of the solution?(MM CdCl2 = 183.31 g / mol)Select one:to.3.73 Mb.0.933 Mc.0.440 Md.0.684 M
A solution is prepared by dissolving 171 g of CdCl2 in water to form 250.0 mL of solution. If the density of the solution is 1.556 g / mL, what is the molarity of the solution?(MM CdCl2 = 183.31 g / mol)Select one:to.3.73 Mb.0.933 Mc.0.440 Md.0.684 M...
5 answers
For a spherically symmetric state of a hydrogen atom, the Schrodinger equation in spherical coordinates is:kee- 2 = Erb2medrz + 2show that the 1s wave function for an electron in hydrogen;rb18Ta3satisfies the Schrodinger equation, with E = -13.6 eV, and r-ao (ground state):Use: Jo = 5.29x10-11m, ke = 8.988x10? Nm2/c2,h = 1.055x10-34 Js, me 9.11x10-31 kg, e = 1.602x10-19 C,and 1 eV = 1.602x10-19 J
For a spherically symmetric state of a hydrogen atom, the Schrodinger equation in spherical coordinates is: kee- 2 = Erb 2me drz + 2 show that the 1s wave function for an electron in hydrogen; rb18 Ta3 satisfies the Schrodinger equation, with E = -13.6 eV, and r-ao (ground state): Use: Jo = 5.29x10-...
4 answers
2.28 If D = (2 + I6r2)a _, calculate fD. ds over hemispherical surface bounded by r = 2 and 0 < 0 < */2.
2.28 If D = (2 + I6r2)a _, calculate fD. ds over hemispherical surface bounded by r = 2 and 0 < 0 < */2....
5 answers
Question 5Below is the Lewis structure for the amino acid histidine_Fill in the blanks by selecting one option from each menu:Part 1: 2_ pointsH H-N ~H 8 H HPart 2 pointsPart 3: pointsPart 4: points:N= HpointsWhat is the local molecular shape of the atom labeled '12"What is the local molecular shape of the atom labeled "2?"What is the approximate value of the bond angle labeled "3?What is the approximate value of the bond angle labeled "4?"
Question 5 Below is the Lewis structure for the amino acid histidine_ Fill in the blanks by selecting one option from each menu: Part 1: 2_ points H H-N ~H 8 H H Part 2 points Part 3: points Part 4: points :N= H points What is the local molecular shape of the atom labeled '12" What is the ...
5 answers
A. If S20,000 is invested at 8%, compounded annually; find the future value in 9 years(Simplify your answer: Round (0 Ihe nearest cent as needed )
a. If S20,000 is invested at 8%, compounded annually; find the future value in 9 years (Simplify your answer: Round (0 Ihe nearest cent as needed )...
5 answers
Fiud Round (he angle 1 Minal bctwccn JJASuE 1 1 [ 5) places 1 uecessaly_ (-3,2,1}.
Fiud Round (he angle 1 Minal bctwccn JJASuE 1 1 [ 5) places 1 uecessaly_ (-3,2,1}....

-- 0.023532--