# Math Help - Is this a solution to the differential equation?

1. ## Is this a solution to the differential equation?

I'm not sure. The solutions given are very vague. I think this is the solution to the differential equation.

Thanks.

2. $\frac{y'}{y^3}+\frac1{y^2}=x,$ if $u=\frac1{y^2}\implies u'=-\frac{2y'}{y^2},$ then $-\frac12u'+u=x\implies u'-2u=-2x,$ now $e^{-2x}u'-2e^{-2x}u=-2xe^{-2x},$ and then $\big(u(x)e^{-2x}\big)'=-2xe^{-2x}.$

you can solve the rest now.