What is the solution for y^{''}+4y=16tsin(2t) ?

The solution for y^{''}+4y=16tsin(2t) is y=c_{1}cos(2t)+c_{2}sin(2t)-2t^2cos(2t)+tsin(2t)

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y^{''}+4y=16tsin(2t)

y^{^{''}} + 4 y = 16 t sin (2 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - 2 t^{2} cos (2 t) + t sin (2 t)

Solution steps

y^{''} (t) + 4 y = 16 t sin (2 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) - 2 t^{2} cos (2 t) + t sin (2 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - 2 t^{2} cos (2 t) + t sin (2 t)

What is the solution for y^{''}+4y=16tsin(2t) ?
The solution for y^{''}+4y=16tsin(2t) is y=c_{1}cos(2t)+c_{2}sin(2t)-2t^2cos(2t)+tsin(2t)