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    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)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:42 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/differential-equation-natural-log-7055

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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 ...

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    A differential equation with a Natural Log is solved

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