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

The solution for y^{''}-3y^'=2x+5-e^{3x} is y=c_{1}e^{3x}+c_{2}+(-x^2-e^{3x}x)/3-(17x)/9

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

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

y = c_{1} e^{3 x} + c_{2} + \frac{- x ^{2} - e ^{3 x} x}{3} - \frac{17 x}{9}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} + \frac{- x ^{2} - e ^{3 x} x}{3} - \frac{17 x}{9}

y = c_{1} e^{3 x} + c_{2} + \frac{- x ^{2} - e ^{3 x} x}{3} - \frac{17 x}{9}

y^{^{''}} - y^{^{'}} - 6 y = 2 e^{3 t}

y^{^{'''}} - 3 y^{^{'}} - 2 y = 9 e^{- x}

y^{^{''}} + y = 2 sin (2 t), y (0) = 11, y^{^{'}} (0) = 0

y^{^{''}} + y = e^{- 2 t} sin (t) + t \cdot cos (t)

y^{^{''}} - 4 y^{^{'}} = 8 e^{6} x (x - 1)

What is the solution for y^{''}-3y^'=2x+5-e^{3x} ?
The solution for y^{''}-3y^'=2x+5-e^{3x} is y=c_{1}e^{3x}+c_{2}+(-x^2-e^{3x}x)/3-(17x)/9