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Solve [he equation tho interval 050<21 tan 8 ' 1J( co3' 1) =0 bory nsut Doron Vou choico Sulect tha correct choice andKolulOrt set $0927 * 4, #odod Ty...

Question

Solve [he equation tho interval 050<21 tan 8 ' 1J( co3' 1) =0 bory nsut Doron Vou choico Sulect tha correct choice andKolulOrt set $0927 * 4, #odod Typo Your Kanntt 0Kct Arskla (Shplity Your nnixer separale anshers &5 needod ) exniussin UJ . comnie inoro no aolutan en tNs inlerval 0 B.

Solve [he equation tho interval 050<21 tan 8 ' 1J( co3' 1) =0 bory nsut Doron Vou choico Sulect tha correct choice and KolulOrt set $ 0927 * 4, #odod Typo Your Kanntt 0Kct Arskla (Shplity Your nnixer separale anshers &5 needod ) exniussin UJ . comnie inoro no aolutan en tNs inlerval 0 B.



Answers

(a) Solve the initial-value problem $$ \begin{aligned} x^{2} y^{\prime \prime}-x y^{\prime}+5 y &=0 \\ y(1)=\sqrt{2}, & y^{\prime}(1)=3 \sqrt{2} \end{aligned} $$ and show that your solution can be written in the form
$$ y(x)=2 x \cos (2 \ln x-\pi / 4) $$ (b) Determine all zeros of $y(x)$ (c) $\diamond$ Sketch the corresponding solution curve on the interval $[0.001,16],$ and verify the zeros in the interval [3,16]

In the execution, we have to find a solution of the given differential equation that is courses square X into divide by dx -Y. into 10 two X is equal to cause four X. This is a differential equation we have given. Now I'm going to divide this by courses square X. So we get this is divided by D X minus. Why into this is 10 2 weeks into shaky square X equals to this becomes courses square X. This is the differential equation. Now in the execution, In this situation we is -102 x into six square x. and Joey's courses square X. Now I'm going to find the integral factor and it is you wanna e to the power integration P. D X. So this is, It was the integration of -102 weeks and This can be written as upon 1 -1 many square X. Sorry, this is no tent works. I am writing The formula of 10. To accept this is 10 x into two and this is shaky square X. Dx. So this will comes out to be logged off one minus any square X. And this is into the power. So the integral factor finally comes to be 1 -10 sq X. This is the integral factor. No, we know their solution of the equation is given by. That is why into integral factor is equals two. Integration of you into integral factor into the X. Now put all the values. So why integral factories one minus 10 square X in the Z equals to chew it courses square X. And this is one Danny square X. Dx. No, I can write it as Why into 1 -10 sq X. Yes equals two. This is one upon shaky square X. So this is one minus tiny square X upon And shake his credits can be bitterness one plus any square X B X. Now this will come out to the integration of course two X. DX. So this is Why into one. My understanding Square X. So finally we get why is it was too Why into 1 -10 sq X. And this is sigh into X by X plus C. Cynics. Sorry, sign two. works by two Plus C. This is the solution. Now we have to find that value of C. So we have given that at X equals two by by six. Why is three route 3 x 8? This is given to us. So now put in this equation. So we get this is three rule three by 18 to 1 minus one by three Equals 2. 1 x two and 2 row three x 2 plus. See from here we get sees equals to zero. So finally our solution is that is to y into 1 -10 sq X is equal to sign to work. This is the solution of the given differential equation, and this is our answer for this solution. So this is given an options. These options, if the correct answer, Thank you.

Danny Square eggs flows three times than eggs plus one equal toe zero in discussion. We have to use the Kartik formula to find all solution off the equation in the interval x greater than an equal to zero x less than two to pipe. Now we use quite a formula. So directs equal toe negative B plus minus square root Be square negative four times a c. A phone to a. Here is the confession off 10 square eggs and he is the coefficient off 10 eggs and constant value is C So now we put that value in the in that quality formula and we get 10 X equal to negative three plus minus square root three square negative. Four time one time, one a phone, two time one After simplifying this, we get. So from this formula, we get to value, uh, when we put here positive value and here is negative value. So first we get positive. Then after that, we will take negative sign. So we get to negative 2.618 and negative 0.3 82 when we find X arc negative 2.618 So we get execute toe Maga, do one point 2059 and execute do negative 0.38 for 0.36 48 We can take negative value Use negative. We'll lose so you can see that here the both value is negative. So gun eggs, you will be negative in the second current and fold current. So we know that eggs Why negative one point 2359 equal toe 1.936 nine. Now we see for the fourth current. So we know that two pi negative 1.2359 equal toe five point zoo 798 Now we do for X equal to negative 0.3648 So we know that x equal toe by negative 0.3648 equal to two point 7780 No, we see For the fourth quadrant X equal due to buy negative 3.3648 equal to 5.9209 So financial is X equal to 1.9369 2.7780 5.798 and 5.9229 eighties over final answer

In this solution, we have to find all solution off the equation. Two times six square eggs close, then square eggs Negative three equal to zero and into it is for this equation eggs greater than an equal to zero eggs. Let them do to buy. Now it's simplified that equation. So we know that sick square eggs equal toe one blows, then squared x It is a technocratic identity. So now we put hear that values to plus two times. Then squat eggs loose Danny square eggs Negative three equal to zero. Now we combine like terms. So we get three times, then squad eggs Negative one equal to see you now We ate one to the both sides. Then we get three times. Then square eggs equal toe one. Now we divide both sides by three. Then we get then square eggs equal Do one upon three we have to take is squired to the both sides. So we get then eggs equal toe us minus one upon square root three. So we know that then eggs equal toe positive one upon is quite a tree Or then eggs equal do negative one. A bomb squired three so Now we find the eggs. So here you can see that Dan X equal do wanna ponce quality. So Dynex give us positive value And we know that the first current and third Cornyn use positive value for 10 so x equal do by upon six for the 1st 1st point and for the third corner x equal do bye flows £5.6 equal do seven by upon six. Now here is negative value for 10 x So we know that it will be in second and fourth Quarante so but exit will do Bye. Negative by upon six. Then we get five by about six for the fourth cordant X equal to Dubai negative by pawn six equal toe 11 by upon six So x equal do by upon six, 55 upon six, 75.6 and a level by upon six So it is our final answer

Three time Danny Square eggs plus four times dan eggs. Negative four equal to sue. So we have to find all solution off the equation in the interval, x greater than an equal to zero bags less than 22 pi. And we have to use the quality formula in discussion. So we know that then eggs equal toe negative B plus minus square root the square negative four times a c upon two times a so be equal toe the coefficients off 10 x and a is the coefficient off Steny Square X and she is the constant, which is negative hope So now we put that value here. So we get 10 eggs, equal toe negative fool plus minus square root foursquare negative. Full time. Three times negative. Four bone two times three. Now we simplify this on. We get 10 eggs equal to negative too, and to a born tree. Now we use the graphing calculator for finding the value off eggs, equal toe or 10 negative two and X equal toe all then two upon three so x equal to negative one point one Jew seven one and eggs are 10, two upon three. So actually is executed toe zero find 58 79 So here is a negative value, so you can't use negative value. So here you can see that Ben eggs equal toe to upon trees for the positive value we have to find execute toe bye blows 2.58 79 because 10 x, it will be positive in the third current. So three point 73 pseudo so no, you can see that here is a negative value X equal to negative 1.1071 and 10 x equal to negative two So 10 will be negative in the second quarter and fourth quarante So we know that eggs equal toe by negative 1.1071 for the second quarter and we get 2.62 36 for the fourth quadrant X equal toe by to buy negative 1.13 or 71 equal toe, five points. 1786 So our final answer is executed. Toe 0.5879 three 0.7307 2.6236 and 5.1786 It is over for I'll answer


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