What is the solution for y^{''}+16y^'=x+e^{2x} ?

The solution for y^{''}+16y^'=x+e^{2x} is y=c_{1}+c_{2}e^{-16x}+(x^2)/(32)-x/(256)+1/36 e^{2x}

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y^{''}+16y^'=x+e^{2x}

y^{^{''}} + 16 y^{^{'}} = x + e^{2 x}

y = c_{1} + c_{2} e^{- 16 x} + \frac{x ^{2}}{32} - \frac{x}{256} + \frac{1}{36} e^{2 x}

Solution steps

y^{''} (x) + 16 y^{'} (x) = x + e^{2 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 16 x} + \frac{x ^{2}}{32} - \frac{x}{256} + \frac{1}{36} e^{2 x}

y = c_{1} + c_{2} e^{- 16 x} + \frac{x ^{2}}{32} - \frac{x}{256} + \frac{1}{36} e^{2 x}

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{x}

y^{^{''}} - 7 y^{^{'}} + 10 y = 6 x + e^{2 x}

4 y^{^{''}} - 2 y^{^{'}} = 4 x, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} - 12 y = (4 x + 7) e^{- 2 x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{3 x}

What is the solution for y^{''}+16y^'=x+e^{2x} ?
The solution for y^{''}+16y^'=x+e^{2x} is y=c_{1}+c_{2}e^{-16x}+(x^2)/(32)-x/(256)+1/36 e^{2x}