Question

Find the general solution (implicit if necessary, explicit if convenient) to the differential equation:

dy/dx + 2xy = 0

Answer 1

We can rewrite the differential equation as:

dy/dx = −2x

This is a separable equation, and so after a little algebra we can write it as

dy/y = −2xdx.

Taking the antiderivative of both sides we get:

Exponentiating both sides, and being a little sloppy with the unknown constant C,² we get: 

y = Ce−^x2 .