What is the solution for y^{''}-5y^'-14y=e^x(x+1) ?

The solution for y^{''}-5y^'-14y=e^x(x+1) is y=c_{1}e^{7x}+c_{2}e^{-2x}-(e^xx)/(18)-5/108 e^x

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y^{''}-5y^'-14y=e^x(x+1)

y^{^{''}} - 5 y^{^{'}} - 14 y = e^{x} (x + 1)

y = c_{1} e^{7 x} + c_{2} e^{- 2 x} - \frac{e ^{x} x}{18} - \frac{5}{108} e^{x}

Solution steps

y^{''} (x) - 5 y^{'} (x) - 14 y = e^{x} (x + 1)

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{- 2 x} - \frac{e ^{x} x}{18} - \frac{5}{108} e^{x}

y = c_{1} e^{7 x} + c_{2} e^{- 2 x} - \frac{e ^{x} x}{18} - \frac{5}{108} e^{x}

What is the solution for y^{''}-5y^'-14y=e^x(x+1) ?
The solution for y^{''}-5y^'-14y=e^x(x+1) is y=c_{1}e^{7x}+c_{2}e^{-2x}-(e^xx)/(18)-5/108 e^x