Question

I have a initial value problem：dy/dx + y/x= -1, y(1)=1. Find the integrating factor and the solution of the problem. Please help me for the solution.

Answer 1

\[\frac{\text dy}{\text dx} +\frac1x y= -1\]

Answer 2

the integrating factor of an equation of the form
\[y^\prime+p(x)y=q(x)\]is\[\mu(x)=e^{\int p(x)\text dx}\]