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

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

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y^{''}+y=t+tsin(t)

y^{^{''}} + y = t + t sin (t)

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

Solution steps

y^{''} (t) + y = t + t sin (t)

Solve linear ODE:

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

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

y^{^{''}} + 11 y^{^{'}} + 18 y = 5 sin (3 x)

y^{^{''}} - 9 y^{^{'}} = 81 x^{2} + 7

y^{^{''}} + y = sec^{3} (x), y (0) = 1

- y^{^{''}} + 10 y^{^{'}} + 25 y = 30 x + 3

y^{^{''}} + 4 y = 5 sec (2 x)

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