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

The solution for y^{''}+5y^'+6y=10sin(x) is y=c_{1}e^{-2x}+c_{2}e^{-3x}+sin(x)-cos(x)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}+5y^'+6y=10sin(x) ?
The solution for y^{''}+5y^'+6y=10sin(x) is y=c_{1}e^{-2x}+c_{2}e^{-3x}+sin(x)-cos(x)