What is the solution for y^{''}-5y^'-6y=3cos(x)+19sin(x) ?

The solution for y^{''}-5y^'-6y=3cos(x)+19sin(x) is y=c_{1}e^{6x}+c_{2}e^{-x}-2sin(x)+cos(x)

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y^{''}-5y^'-6y=3cos(x)+19sin(x)

y^{^{''}} - 5 y^{^{'}} - 6 y = 3 cos (x) + 19 sin (x)

y = c_{1} e^{6 x} + c_{2} e^{- x} - 2 sin (x) + cos (x)

Solution steps

y^{''} (x) - 5 y^{'} (x) - 6 y = 3 cos (x) + 19 sin (x)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- x} - 2 sin (x) + cos (x)

y = c_{1} e^{6 x} + c_{2} e^{- x} - 2 sin (x) + cos (x)

What is the solution for y^{''}-5y^'-6y=3cos(x)+19sin(x) ?
The solution for y^{''}-5y^'-6y=3cos(x)+19sin(x) is y=c_{1}e^{6x}+c_{2}e^{-x}-2sin(x)+cos(x)