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

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

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y^{''}+y=2cos(t)

y^{^{''}} + y = 2 cos (t)

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

Solution steps

y^{''} (t) + y = 2 cos (t)

Solve linear ODE:

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

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

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

y^{^{''''}} + 9 y^{^{''}} = sec^{2} (3 t)

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 x + 7

y^{^{''}} - 6 y^{^{'}} - 7 y = - 9 e^{- 2 x}

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

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