(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] 2y\prime\prime +2y\prime + y = 4 \sqrt{x}[/tex]

3. The attempt at a solution

charecteristic equation: [tex] x^2+x+\frac{1}{2}[/tex]

roots: [tex]\frac{1}{2}\pm\frac{1}{2}i[/tex]

homogenous solution: [tex] a \sin{\frac{1}{2}x} + b \cos{\frac{1}{2}x}[/tex]

Wronskian: [tex] \left(\begin{array}{cc}\sin{\frac{1}{2}x}&\cos{\frac{1}{2}x}\\\frac{1}{2}\cos{\frac{1}{2}x}&-\frac{1}{2}\sin{\frac{1}{2}x}\end{array}\right) = -\frac{1}{2}[/tex]

It would be nice to know if up to here, everyone else gets the same answer. After this I get into non elementary functions which is no where near the level of difficulty included within the course I'm taking. I haven't attempted to solve what comes next, frankly because I have no clue where to even begin. I think I probably made a mistake above, if someone can point me in the right direction that would be awesome. The method used is variation of parameters.

[tex]y_{1}=\sin{\frac{1}{2}x} [/tex]

[tex]y_{2}=\cos{\frac{1}{2}x}[/tex]

[tex] u_{1} = \int{4\sqrt{x}\cos{\frac{1}{2}x}dx} [/tex]

[tex]u_{2} = \int{-4\sqrt{x}\sin{\frac{1}{2}x}dx}[/tex]

ick

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# Homework Help: Variations of parameters

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