What is the solution for y^{''}-y^'-6y=32sin(3x) ?

The solution for y^{''}-y^'-6y=32sin(3x) is y=c_{1}e^{3x}+c_{2}e^{-2x}-80/39 sin(3x)+16/39 cos(3x)

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y^{''}-y^'-6y=32sin(3x)

y^{^{''}} - y^{^{'}} - 6 y = 32 sin (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{80}{39} sin (3 x) + \frac{16}{39} cos (3 x)

Solution steps

y^{''} (x) - y^{'} (x) - 6 y = 32 sin (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{80}{39} sin (3 x) + \frac{16}{39} cos (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{80}{39} sin (3 x) + \frac{16}{39} cos (3 x)

What is the solution for y^{''}-y^'-6y=32sin(3x) ?
The solution for y^{''}-y^'-6y=32sin(3x) is y=c_{1}e^{3x}+c_{2}e^{-2x}-80/39 sin(3x)+16/39 cos(3x)