What is the solution for y^{''}+4y=9t ?

The solution for y^{''}+4y=9t is y=c_{1}cos(2t)+c_{2}sin(2t)+(9t)/4

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y^{''}+4y=9t

y^{^{''}} + 4 y = 9 t

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{9 t}{4}

Solution steps

y^{''} (t) + 4 y = 9 t

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{9 t}{4}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{9 t}{4}

y^{^{''}} + 4 y = 3 csc (x)

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = 2 x e^{- x}

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

y^{^{''}} - 5 y^{^{'}} + 6 y = (x + 1) e^{- x}

y^{^{''}} + 3 y^{^{'}} = 3 x e^{- 3 x}

What is the solution for y^{''}+4y=9t ?
The solution for y^{''}+4y=9t is y=c_{1}cos(2t)+c_{2}sin(2t)+(9t)/4