What is the solution for y^{''}+5y^'-6y=2sin(4x) ?

The solution for y^{''}+5y^'-6y=2sin(4x) is y=c_{1}e^x+c_{2}e^{-6x}-11/221 sin(4x)-10/221 cos(4x)

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y^{''}+5y^'-6y=2sin(4x)

y^{^{''}} + 5 y^{^{'}} - 6 y = 2 sin (4 x)

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{11}{221} sin (4 x) - \frac{10}{221} cos (4 x)

Solution steps

y^{''} (x) + 5 y^{'} (x) - 6 y = 2 sin (4 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{11}{221} sin (4 x) - \frac{10}{221} cos (4 x)

y = c_{1} e^{x} + c_{2} e^{- 6 x} - \frac{11}{221} sin (4 x) - \frac{10}{221} cos (4 x)

y^{^{'''}} + 3 y^{^{''}} - 9 y^{^{'}} + 5 y = 4 e^{- x} + cos (x)

y^{^{''}} + 3 y^{^{'}} + 4 y = 20 x + 33

y^{^{''}} - 2 y^{^{'}} + 5 y = cos (4 x) + 1

x^{^{''}} + x = 5 cos (t)

y^{^{''}} - 2 y^{^{'}} + y = 3

What is the solution for y^{''}+5y^'-6y=2sin(4x) ?
The solution for y^{''}+5y^'-6y=2sin(4x) is y=c_{1}e^x+c_{2}e^{-6x}-11/221 sin(4x)-10/221 cos(4x)