Answer:Step-by-step explanation:Let's rewrite this with dy/dx in place of y', since they mean the same thing. But to solve a differential we will need to take the antiderivative by separation to find the general solution.[tex]\frac{dy}{dx}+xy=x[/tex]The goal is to get the x stuff on one side and the y stuff on the other side by separation. But we have an xy term there that we need to be able to break apart. So let's get everything on one side separate from the dy/dx and take it from there.[tex]\frac{dy}{dx}=x-xy[/tex]Now we can factor out the x:[tex]\frac{dy}{dx}=x(1-y)[/tex]And now we can separate:[tex]\frac{dy}{(1-y)}=x dx[/tex]Now we solve by taking the antiderivative of both sides:[tex]\int\ {\frac{1}{1-y}dy }=\int\ {x} \, dx[/tex]On the left side, the antiderivative of the derivative of y cancels out, and the other part takes on the form of the natural log, while we follow the power rule backwards on the right to integrate x:[tex]ln(1-y)=\frac{1}{2}x^2+C[/tex]That's the general solution. Not sure what your book has you solving for. Some books solve for the constant, C. Some solve for y when applicable. I'm leaving it like it is.