What is the solution for y^{''}+6y^'+10y=180sin(2x) ?

The solution for y^{''}+6y^'+10y=180sin(2x) is y=e^{-3x}(c_{1}cos(x)+c_{2}sin(x))+6sin(2x)-12cos(2x)

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y^{''}+6y^'+10y=180sin(2x)

y^{^{''}} + 6 y^{^{'}} + 10 y = 180 sin (2 x)

y = e^{- 3 x} (c_{1} cos (x) + c_{2} sin (x)) + 6 sin (2 x) - 12 cos (2 x)

Solution steps

y^{''} (x) + 6 y^{'} (x) + 10 y = 180 sin (2 x)

Solve linear ODE:

y = e^{- 3 x} (c_{1} cos (x) + c_{2} sin (x)) + 6 sin (2 x) - 12 cos (2 x)

y = e^{- 3 x} (c_{1} cos (x) + c_{2} sin (x)) + 6 sin (2 x) - 12 cos (2 x)

What is the solution for y^{''}+6y^'+10y=180sin(2x) ?
The solution for y^{''}+6y^'+10y=180sin(2x) is y=e^{-3x}(c_{1}cos(x)+c_{2}sin(x))+6sin(2x)-12cos(2x)