What is the solution for 5y^{''}-15y=10e^x ?

The solution for 5y^{''}-15y=10e^x is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-e^x

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5y^{''}-15y=10e^x

5 y^{^{''}} - 15 y = 10 e^{x}

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

Solution steps

5 y^{''} (x) - 15 y = 10 e^{x}

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = e^{- x} (2 x - 5)

y^{^{''}} - y^{^{'}} = 16 e^{3 x}

y^{^{''}} + 2 y^{^{'}} + 2 y = 5 sin (x) - 10 x e^{x}

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (x)

y^{^{''}} + 49 y = t^{2} cos (7 t) + t e^{- 7 t}

What is the solution for 5y^{''}-15y=10e^x ?
The solution for 5y^{''}-15y=10e^x is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-e^x