What is the solution for y^{''}+y=8e^{-6x} ?

The solution for y^{''}+y=8e^{-6x} is y=c_{1}cos(x)+c_{2}sin(x)+8/37 e^{-6x}

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y^{''}+y=8e^{-6x}

y^{^{''}} + y = 8 e^{- 6 x}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{8}{37} e^{- 6 x}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{8}{37} e^{- 6 x}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{8}{37} e^{- 6 x}

(d^{2} - 1) \cdot y = x \cdot e^{x} + cos^{2} (x) + x^{2}

y^{^{''}} + 2 y^{^{'}} + y = 8 e^{x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 2 y = x^{2} + 1

y^{^{''}} - y^{^{'}} = \frac{1}{e ^{x} + 1}

y^{^{''}} - 10 y^{^{'}} + 25 y = 3 e^{5 t}

What is the solution for y^{''}+y=8e^{-6x} ?
The solution for y^{''}+y=8e^{-6x} is y=c_{1}cos(x)+c_{2}sin(x)+8/37 e^{-6x}