What is the solution for 4y-y^{''}=10e^{(-3x)} ?

The solution for 4y-y^{''}=10e^{(-3x)} is y=c_{1}e^{2x}+c_{2}e^{-2x}-2e^{-3x}

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4y-y^{''}=10e^{(-3x)}

4 y - y^{^{''}} = 10 e^{(- 3 x)}

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

Solution steps

4 y - y^{''} (x) = 10 e^{(- 3 x)}

Solve linear ODE:

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

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

What is the solution for 4y-y^{''}=10e^{(-3x)} ?
The solution for 4y-y^{''}=10e^{(-3x)} is y=c_{1}e^{2x}+c_{2}e^{-2x}-2e^{-3x}