Solve for dy/dx+y/x=1/x
I'd like to see the correct way to solve it. I did it a ridiculous way and ended up with the answer, but I don't want to spend so much time next time.
General formula is y=e^-(P(x)dx)*int[(Q(x)e^(P(x)dx)dx], no?
P(x)y=y/x so P(x)=1/x
Q(x)=1/x so Q(x)=1/x as well
the integrating factor is = e^int[(P(x)dx)] = e^int[1/x] = e^[ln(x)] = x ... right?
I should just be able to plug in and solve, right?