I have this really simple differential equation. It needs to be in the form y'+ p(x)y=q(x) to solve it as a linear first order ODE. I am almost embarassed to ask, but I can't seem to get it in exactly this form. Read below.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

y'+3y=2x(e^-3x)

Need y'+ p(x)y=q(x)

3. The attempt at a solution

Divide both sides by 2x, gives

y'/2x + 3y/2x = e^-3x

Now here I have y' multiplied by the function 1/2x, but according to the proper linear first order ODE form, Y' needs to be by itself.

Can you give me some tips on how to achieve this? I don't know why I can't see it, its probably very simple, but whatever the algebraic manipulation is for this, I seem to have forgotten it.

Thank you.

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# Homework Help: Easy algebra question related to Differential equations

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