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

The solution for y^{''}+5y^'=x-2-3e^{2x} is y=c_{1}+c_{2}e^{-5x}+(x^2)/(10)-(11x)/(25)-3/14 e^{2x}

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y^{''}+5y^'=x-2-3e^{2x}

y^{^{''}} + 5 y^{^{'}} = x - 2 - 3 e^{2 x}

y = c_{1} + c_{2} e^{- 5 x} + \frac{x ^{2}}{10} - \frac{11 x}{25} - \frac{3}{14} e^{2 x}

Solution steps

y^{''} (x) + 5 y^{'} (x) = x - 2 - 3 e^{2 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 x} + \frac{x ^{2}}{10} - \frac{11 x}{25} - \frac{3}{14} e^{2 x}

y = c_{1} + c_{2} e^{- 5 x} + \frac{x ^{2}}{10} - \frac{11 x}{25} - \frac{3}{14} e^{2 x}

x^{^{''}} + 3 x^{^{'}} + 33 x = 8 cos (5 t)

x^{^{''}} + 16 x = cos (4 t)

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

y^{^{''}} + 4 y = - 12 sin (2 x), y (0) = 1.8, y^{^{'}} (0) = 5

y^{^{''}} - 11 y^{^{'}} + 24 y = 13 + 24 x

What is the solution for y^{''}+5y^'=x-2-3e^{2x} ?
The solution for y^{''}+5y^'=x-2-3e^{2x} is y=c_{1}+c_{2}e^{-5x}+(x^2)/(10)-(11x)/(25)-3/14 e^{2x}