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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} + 6 y^{^{'}} + 5 y = - 7 t e^{4 t}

y^{^{''}} + 10 y^{^{'}} + 25 y = 14 \cdot e^{5 x}

3 x^{^{''}} + 48 x = 153 e^{- 2 t} cos (4 t)

y^{^{''}} - 9 y = 4 e^{3 t}, y (0) = 0, y^{^{'}} (0) = - 1

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