What is the solution for y^{''}+y=3cos(t) ?

The solution for y^{''}+y=3cos(t) is y=c_{1}cos(t)+c_{2}sin(t)+(3tsin(t))/2

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y^{''}+y=3cos(t)

y^{^{''}} + y = 3 cos (t)

y = c_{1} cos (t) + c_{2} sin (t) + \frac{3 t sin ( t )}{2}

Solution steps

y^{''} (t) + y = 3 cos (t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + \frac{3 t sin ( t )}{2}

y = c_{1} cos (t) + c_{2} sin (t) + \frac{3 t sin ( t )}{2}

y^{^{''}} - 16 y = sin (2 x) - 3 cos (2 x)

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} lo g_{e} (1 + x^{2})

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

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

y^{^{''}} - 6 y^{^{'}} + 8 y = 64 x^{2}

What is the solution for y^{''}+y=3cos(t) ?
The solution for y^{''}+y=3cos(t) is y=c_{1}cos(t)+c_{2}sin(t)+(3tsin(t))/2