What is the solution for y^{''}+8y^'+15y=cos(x) ?

The solution for y^{''}+8y^'+15y=cos(x) is y=c_{1}e^{-3x}+c_{2}e^{-5x}+2/65 sin(x)+7/130 cos(x)

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y^{''}+8y^'+15y=cos(x)

y^{^{''}} + 8 y^{^{'}} + 15 y = cos (x)

y = c_{1} e^{- 3 x} + c_{2} e^{- 5 x} + \frac{2}{65} sin (x) + \frac{7}{130} cos (x)

Solution steps

y^{''} (x) + 8 y^{'} (x) + 15 y = cos (x)

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- 5 x} + \frac{2}{65} sin (x) + \frac{7}{130} cos (x)

y = c_{1} e^{- 3 x} + c_{2} e^{- 5 x} + \frac{2}{65} sin (x) + \frac{7}{130} cos (x)

f (x) = 3 x cos (x), (π, - 3 π)

(1 - e^{- x} - x e^{- x})^{^{'}}

\frac{\partial}{\partial x} (x^{3} y - x)

\int \frac{x ^{2} + 1}{x ^{3} + 3 x} d x

\int e^{x} \cdot (- 3) e^{e^{x} + 2} d x

What is the solution for y^{''}+8y^'+15y=cos(x) ?
The solution for y^{''}+8y^'+15y=cos(x) is y=c_{1}e^{-3x}+c_{2}e^{-5x}+2/65 sin(x)+7/130 cos(x)