What is the solution for y^{''}+9y=5sin(x) ?

The solution for y^{''}+9y=5sin(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+5/8 sin(x)

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y^{''}+9y=5sin(x)

y^{^{''}} + 9 y = 5 sin (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{5}{8} sin (x)

Solution steps

y^{''} (x) + 9 y = 5 sin (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{5}{8} sin (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{5}{8} sin (x)

y^{^{''}} + 7 y^{^{'}} + 10 y = x e^{- 2 x}

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

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- t}

y^{^{''}} - 4 y + 8 y = 4 sin (x)

y^{^{''}} - 8 y^{^{'}} \cdot + 25 = 0

What is the solution for y^{''}+9y=5sin(x) ?
The solution for y^{''}+9y=5sin(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+5/8 sin(x)