What is the solution for y^{''}+10y^'+16y=949sin(3x) ?

The solution for y^{''}+10y^'+16y=949sin(3x) is y=c_{1}e^{-2x}+c_{2}e^{-8x}+7sin(3x)-30cos(3x)

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y^{''}+10y^'+16y=949sin(3x)

y^{^{''}} + 10 y^{^{'}} + 16 y = 949 sin (3 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + 7 sin (3 x) - 30 cos (3 x)

Solution steps

y^{''} (x) + 10 y^{'} (x) + 16 y = 949 sin (3 x)

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + 7 sin (3 x) - 30 cos (3 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + 7 sin (3 x) - 30 cos (3 x)

y^{^{''}} + 6 y^{^{'}} + 25 y = 100 cos (4 t)

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 5} e^{3 t}

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- x} + 4 x

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{- t}

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 50, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}+10y^'+16y=949sin(3x) ?
The solution for y^{''}+10y^'+16y=949sin(3x) is y=c_{1}e^{-2x}+c_{2}e^{-8x}+7sin(3x)-30cos(3x)