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

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- az_lenderLv 710 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).

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- VamanLv 710 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.

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- Anonymous10 months ago
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