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AB Calculus

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So I'm supposed to verify the solution of the differential equation. The solution is y=e^(-x). The differential equation is 3y' + 4y = e^(-x). What is the problem asking me to do here?

  • AB Calculus -

    plug in y to see whether it satisfies the differential equation

    y = e^(-x)
    y' = -e^(-x)

    3y' + 4y = -3e^(-x) + 4e^(-x) = e^-x

    so, it does satisfy it.

  • AB Calculus -

    Oh, okay. I get it now. Thanks!

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