What is the solution for y^{''}+y=sqrt(2)sin(sqrt(2)x) ?

The solution for y^{''}+y=sqrt(2)sin(sqrt(2)x) is y=c_{1}cos(x)+c_{2}sin(x)-sqrt(2)sin(sqrt(2)x)

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{'''}} + 49 y^{^{'}} = 5 x + 6

y^{^{''}} - 6 y^{^{'}} + 9 y = x^{- 4} \cdot e^{3} x

3 y^{^{''}} + 4 y = 3 e^{3} x

y^{^{''}} - 2 y^{^{'}} + 2 y = e x, y (\frac{π}{2}) = 0, y (0) = 0

y^{^{''}} + y^{^{'}} - 6 y = 18

What is the solution for y^{''}+y=sqrt(2)sin(sqrt(2)x) ?
The solution for y^{''}+y=sqrt(2)sin(sqrt(2)x) is y=c_{1}cos(x)+c_{2}sin(x)-sqrt(2)sin(sqrt(2)x)