- #1

- 5

- 1

^{x/2}√(1-x

^{2})

Can anyone tell me how to solve this step by step?

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- Thread starter GoodEngineering
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- #1

- 5

- 1

Can anyone tell me how to solve this step by step?

- #2

fresh_42

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You first solve the homogeneous version.

- #3

HallsofIvy

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To solve the entire equation use "variation of parameters": Look for a solution of the form [tex]y(x)= u(x)e^{-x/4}[/tex]. Then [tex]y'= u'e^{-x/4}- (u/4)e^{-x/4}= (u'- u/4)e^{-x/4}[/tex] so the equation becomes [tex](4u'- u)e^{-x/4}+ ue^{-x/4}= 4u'e^{-x/4}= e^{x/2}\sqrt{1- x^2}[/tex] so that [tex]u'= \frac{1}{4}e^{3x/4}(1- x^2)^{1/2}[/tex]. Can you integrate that?

- #4

Mark44

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We had to find the general solution for the differential equation. This was the exercise: 4y'' - 4y' + y = e^{x/2}√(1-x^{2})

No. You apparently missed the second-order term 4y''.The "associated homogeneous equation" is -4y'+ y= 0

That's not what we do here. Per our rules (https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/, under Homework Guidelines), you must first make an attempt. Also, homework-type questions should be posted in one of the sections under Homework & Coursework.Can anyone tell me how to solve this step by step?

- #5

HallsofIvy

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Yes, I did miss that! Thanks.

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