What is the solution for y^{''}+8y^'+15y=-6cos(5x) ?

The solution for y^{''}+8y^'+15y=-6cos(5x) is y=c_{1}e^{-3x}+c_{2}e^{-5x}-12/85 sin(5x)+3/85 cos(5x)

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y^{''}+8y^'+15y=-6cos(5x)

y^{^{''}} + 8 y^{^{'}} + 15 y = - 6 cos (5 x)

y = c_{1} e^{- 3 x} + c_{2} e^{- 5 x} - \frac{12}{85} sin (5 x) + \frac{3}{85} cos (5 x)

Solution steps

y^{''} (x) + 8 y^{'} (x) + 15 y = - 6 cos (5 x)

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- 5 x} - \frac{12}{85} sin (5 x) + \frac{3}{85} cos (5 x)

y = c_{1} e^{- 3 x} + c_{2} e^{- 5 x} - \frac{12}{85} sin (5 x) + \frac{3}{85} cos (5 x)

What is the solution for y^{''}+8y^'+15y=-6cos(5x) ?
The solution for y^{''}+8y^'+15y=-6cos(5x) is y=c_{1}e^{-3x}+c_{2}e^{-5x}-12/85 sin(5x)+3/85 cos(5x)