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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = x^{2} - 1

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2} x

y^{^{''}} - 4 y^{^{'}} + 5 y = \frac{2 e ^{2 x}}{sin ( x )}

3 y^{^{''}} - 6 y^{^{'}} + 6 y = e^{x} \cdot sec (x)

y^{^{''}} + y^{^{'}} - 2 y = 12 cos (2 x)

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