# Differential Equation with a Natural Log

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Find a general solution for this differential equation.

Please see the attached file for the fully formatted problem.

dy/dx + 2xy = xe^(-x2+2)

https://brainmass.com/math/calculus-and-analysis/differential-equation-natural-log-7055

#### Solution Preview

Solution. First, we find the general solution for y'+2xy=0, ie.,

dy/dx=-2xy==>dy/y=-2xdx

Integrating on both sides we get,

lny=-x^2+C1.

So y=Ce^(-x^2).

Then, for the diff. equation dy/dx+2xy=xe^(-x^2+x) (1)

We assume that ...

#### Solution Summary

A differential equation with a Natural Log is solved

$2.49