for some reason i am having trouble doing this problem and i think it is really easy:

dy/dx=x+3y

I just don't see what to do can someone help me? thanks

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- Mar 7th 2009, 07:20 PMjarnyDiff eq
for some reason i am having trouble doing this problem and i think it is really easy:

dy/dx=x+3y

I just don't see what to do can someone help me? thanks - Mar 7th 2009, 08:01 PMChris L T521
This is the same as $\displaystyle \frac{\,dy}{\,dx}-3y=x$

This is a linear DE, and the integrating factor is $\displaystyle \varrho\!\left(x\right)=e^{\int 3\,dx}=e^{3x}$

Thus, we now see that $\displaystyle \frac{\,d}{\,dx}\left[ye^{3x}\right]=xe^{3x}$.

Now, integrating both sides yields $\displaystyle ye^{3x}=\int xe^{3x}\,dx$

Can you continue on from here?