What is the solution for y^{''}-3y=e^x ?

The solution for y^{''}-3y=e^x is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-1/2 e^x

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y^{''}-3y=e^x

y^{^{''}} - 3 y = e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{2} e^{x}

Solution steps

y^{''} (x) - 3 y = e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{2} e^{x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{2} e^{x}

What is the solution for y^{''}-3y=e^x ?
The solution for y^{''}-3y=e^x is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-1/2 e^x