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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 4 e^{- 4 t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 3 cos (3 t), y (0) = 2, y^{^{'}} (0) = 3

x^{^{''}} + x = sin (2 t)

y^{^{''}} + 16 y = 11 sec^{2} (4 t)

y^{^{''}} - 4 y^{^{'}} - 12 y = 2 sin (t)

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