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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

(d^{4} - 1) y = e^{x} cos (x)

(d^{2} + 1) y = sec (x) + tan (x)

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

(d^{2} + 9) y = 7 e^{3 x} + 3 x^{2} + 4

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