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
