What is the solution for y^{''}-5y^'+6y=-2e^x ?

The solution for y^{''}-5y^'+6y=-2e^x is y=c_{1}e^{3x}+c_{2}e^{2x}-e^x

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y^{''}-5y^'+6y=-2e^x

y^{^{''}} - 5 y^{^{'}} + 6 y = - 2 e^{x}

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

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = - 2 e^{x}

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{x} sin (x)

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 - 3 e^{x}

y^{^{''}} - y = 4 x^{2} - 1

2 y^{^{''}} + 8 y^{^{'}} + 8 y = e^{- 2 x} + x

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 e^{2 x} + x sin (x)

What is the solution for y^{''}-5y^'+6y=-2e^x ?
The solution for y^{''}-5y^'+6y=-2e^x is y=c_{1}e^{3x}+c_{2}e^{2x}-e^x