What is the solution for y^{''}+y^'-6y=50xe^x ?

The solution for y^{''}+y^'-6y=50xe^x is y=c_{1}e^{2x}+c_{2}e^{-3x}-(25e^xx)/2-75/8 e^x

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y^{''}+y^'-6y=50xe^x

y^{^{''}} + y^{^{'}} - 6 y = 50 x e^{x}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{25 e ^{x} x}{2} - \frac{75}{8} e^{x}

Solution steps

y^{''} (x) + y^{'} (x) - 6 y = 50 x e^{x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{25 e ^{x} x}{2} - \frac{75}{8} e^{x}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{25 e ^{x} x}{2} - \frac{75}{8} e^{x}

What is the solution for y^{''}+y^'-6y=50xe^x ?
The solution for y^{''}+y^'-6y=50xe^x is y=c_{1}e^{2x}+c_{2}e^{-3x}-(25e^xx)/2-75/8 e^x