What is the solution for y^{''}+16y=sin(5x) ?

The solution for y^{''}+16y=sin(5x) is y=c_{1}cos(4x)+c_{2}sin(4x)-1/9 sin(5x)

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y^{''}+16y=sin(5x)

y^{^{''}} + 16 y = sin (5 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{1}{9} sin (5 x)

Solution steps

y^{''} (x) + 16 y = sin (5 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{1}{9} sin (5 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) - \frac{1}{9} sin (5 x)

4 y^{^{''}} - 4 y^{^{'}} - 35 y = cos (2 x)

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

y^{^{''}} - y^{^{'}} + 25 y = 5 sin (5 t)

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{t} cos (t)

y^{^{'''}} + 36 y^{^{'}} = sec (6 x)

What is the solution for y^{''}+16y=sin(5x) ?
The solution for y^{''}+16y=sin(5x) is y=c_{1}cos(4x)+c_{2}sin(4x)-1/9 sin(5x)