What is the solution for y^{''}+9y=4sin(x) ?

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

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y^{''}+9y=4sin(x)

y^{^{''}} + 9 y = 4 sin (x)

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

Solution steps

y^{''} (x) + 9 y = 4 sin (x)

Solve linear ODE:

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

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

\frac{d}{d x} (1 + 5 x)

\frac{\partial}{\partial x} (3 e^{- y} (x^{2} + y^{2}) + 4)

\int \frac{1}{x ( x ^{2} - 16 ) ^{\frac{3}{2}}} d x

f (x) = \frac{cos ( x )}{1 + a sin ( x )}

y = sin (ln (x))

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