What is the solution for y^{''}+6y^'+5y=10cos(x) ?

The solution for y^{''}+6y^'+5y=10cos(x) is y=c_{1}e^{-x}+c_{2}e^{-5x}+15/13 sin(x)+10/13 cos(x)

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y^{''}+6y^'+5y=10cos(x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 10 cos (x)

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{15}{13} sin (x) + \frac{10}{13} cos (x)

Solution steps

y^{''} (x) + 6 y^{'} (x) + 5 y = 10 cos (x)

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{15}{13} sin (x) + \frac{10}{13} cos (x)

y = c_{1} e^{- x} + c_{2} e^{- 5 x} + \frac{15}{13} sin (x) + \frac{10}{13} cos (x)

What is the solution for y^{''}+6y^'+5y=10cos(x) ?
The solution for y^{''}+6y^'+5y=10cos(x) is y=c_{1}e^{-x}+c_{2}e^{-5x}+15/13 sin(x)+10/13 cos(x)