Find Differential Equation by eliminating arbitrary constant from y=x+c1e^x+c2e^-x?

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  • 2 months ago

    dy/dx = 1 + c1*e^x - c2*e^(-x);

    d2y/dx2 = c1*e^x + c2*e^(-x) = y - x.

    The differential equation y" = y-x

    has y = x + c1*e^x + c2*e^(-x) as a solution.

    The only thing wrong with Katherine Malakowski's answer is her error in typing the first derivative (there should be a 1 in it).

  • Vaman
    Lv 7
    2 months ago

    y=x+c1e^x+c2e^-x?

    take the first derivative.

    dy/dx= c1 e^x-c2 e^x. Take the second derivative.

    d^2y/dx^2= c1 e^x + c2 e^-x. Eliminate using the first equation.

    You get

    d^2y/dx^2=y-x. You can write it as y'' -y=-x. This is the differential equation.

  • Anonymous
    2 months ago

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