find the particular solution for y''+25y=50sin(5t)(adsbygoogle = window.adsbygoogle || []).push({});

I am using variation of parameter:

[tex]y_p=U_1e^{5x}+U_2e^{-5x}[/tex]

[tex]y_1=e^{5x},y_1'=5e^{5x},y_2=e^{-5x},y_2'=-5e^{-5x}[/tex]

[tex]U_1=- \int \frac{e^{-5x}50sin(5t)}{-10}=-0.5e^{-5x} (cos5x+sin5x)[/tex]

[tex]U_2= \int \frac{e^{5x}50sin(5t)}{-10}=0.5e^{5x} (cos5x-sin5x)[/tex]

[tex]y_p=-0.5e^{-5x} (cos5x+sin5x) e^{5x}+ 0.5e^{5x} (cos5x-sin5x)e^{-5x}[/tex]

[tex]y_p=-sin5x[/tex]

I know this is wrong because the check doesnt equal 50sin(5t)

any ideas?

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# Homework Help: Dif eq with particular solution

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