What is the solution for y^{''}+4y^'+5y=15x+e^{-x} ?

The solution for y^{''}+4y^'+5y=15x+e^{-x} is y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+3x-12/5+1/2 e^{-x}

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y^{''}+4y^'+5y=15x+e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 x + e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

Solution steps

y^{''} (x) + 4 y^{'} (x) + 5 y = 15 x + e^{- x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

\frac{d}{d x} (\frac{sin ( x )}{1 + sin ( x )})

\int \frac{x ln ( x )}{x ^{2} - 1} d x

\int_{1}^{\infty} (\frac{1}{x ^{3}}) d x

\frac{d y}{d x} x + y = - 2 x^{6} y^{4}

4 \frac{d ^{2} x}{d t ^{2}} - 1 \frac{d x}{d t} - 3 x = 0, x (0) = 1

What is the solution for y^{''}+4y^'+5y=15x+e^{-x} ?
The solution for y^{''}+4y^'+5y=15x+e^{-x} is y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+3x-12/5+1/2 e^{-x}