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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 81 y = cosh (9 x)

y^{^{''}} + 4 y = x e^{x} + x sin (2 x)

y^{^{''}} + 49 y = csc (7 x)

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