What is the solution for y^{''}+9y=18t,y(pi/2)=0,y(0)=0 ?

The solution for y^{''}+9y=18t,y(pi/2)=0,y(0)=0 is y=2t+pisin(3t)

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y^{''}+9y=18t,y(pi/2)=0,y(0)=0

y^{^{''}} + 9 y = 18 t, y (\frac{π}{2}) = 0, y (0) = 0

y = 2 t + π sin (3 t)

Solution steps

y^{''} (t) + 9 y = 18 t

Solve linear ODE:

y = 2 t + π sin (3 t)

y = 2 t + π sin (3 t)

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{- 2} e^{- 2 x}

y^{^{''}} + 16 y = sin (5 x)

4 y^{^{''}} - 4 y^{^{'}} - 35 y = cos (2 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x e^{2 x}

y^{^{''}} - y^{^{'}} + 25 y = 5 sin (5 t)

What is the solution for y^{''}+9y=18t,y(pi/2)=0,y(0)=0 ?
The solution for y^{''}+9y=18t,y(pi/2)=0,y(0)=0 is y=2t+pisin(3t)