We cannot separate the variables, so we hope that it is linear.
It is linear if we can get it in the form



then we can solve it by multiplying by the
integrating factor 

So let's try to get it in that form:







Divide through by -x





So it is a linear differential equation with  and 

Linear differential equations are usually easier if we can
avoid denominators by using negative exponents:



We calculate the integrating factor



We multiply through by the integrating factor 





We integrate both sides:



The right side is easy to integrate.  The left side requires a little
more thinking since we cannot integrate the terms separately.  On the left 
side, we have the integral of the differential of a product 
d(u*v) = u*dv+v*du, where  and , so the left side
integrates to the product  or  and so the general
solution is



Multiply both sides by x²







Edwin