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
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?