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

The solution for y^{''}-y^'-6y=sin(x) is y=c_{1}e^{3x}+c_{2}e^{-2x}-7/50 sin(x)+1/50 cos(x)

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y^{''}-y^'-6y=sin(x)

y^{^{''}} - y^{^{'}} - 6 y = sin (x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{7}{50} sin (x) + \frac{1}{50} cos (x)

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = sin (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{7}{50} sin (x) + \frac{1}{50} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{7}{50} sin (x) + \frac{1}{50} cos (x)

What is the solution for y^{''}-y^'-6y=sin(x) ?
The solution for y^{''}-y^'-6y=sin(x) is y=c_{1}e^{3x}+c_{2}e^{-2x}-7/50 sin(x)+1/50 cos(x)