What is the solution for y^{''}+4y^'+5y=5x+3e^{-x} ?

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

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

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

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + x - \frac{4}{5} + \frac{3}{2} e^{- x}

Solution steps

y^{''} (x) + 4 y^{'} (x) + 5 y = 5 x + 3 e^{- x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + x - \frac{4}{5} + \frac{3}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + x - \frac{4}{5} + \frac{3}{2} e^{- x}

2 t \frac{d y}{d t} + y = t^{4}

x \to - 2 - lim (4 x^{2} - 7)

\int \frac{sin ( 2 x )}{cos ^{2} ( x )} d x

x \to 0 lim (sin^{2} (x))

e^{3 t s i n (2 t)}

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