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Differential Equation with a Natural Log

Find a general solution for this differential equation.
Please see the attached file for the fully formatted problem.
dy/dx + 2xy = xe^(-x2+2)

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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

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