What is the solution for y^{''}+9y=2sin(x)+cos(x) ?

The solution for y^{''}+9y=2sin(x)+cos(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+1/4 sin(x)+1/8 cos(x)

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y^{''}+9y=2sin(x)+cos(x)

y^{^{''}} + 9 y = 2 sin (x) + cos (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{4} sin (x) + \frac{1}{8} cos (x)

Solution steps

y^{''} (x) + 9 y = 2 sin (x) + cos (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{4} sin (x) + \frac{1}{8} cos (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{4} sin (x) + \frac{1}{8} cos (x)

\frac{d y}{d x} - x y = x

25 y^{^{''}} + 90 y^{^{'}} + 81 y = 0

\frac{d}{d x} (65611 2^{x})

\int \frac{1}{sin ( 2 x )} d x

\frac{d}{d x} (3 sec (8 x))

What is the solution for y^{''}+9y=2sin(x)+cos(x) ?
The solution for y^{''}+9y=2sin(x)+cos(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+1/4 sin(x)+1/8 cos(x)