What is the solution for y^{''}+9y=3sin(2x) ?

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

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y^{''}+9y=3sin(2x)

y^{^{''}} + 9 y = 3 sin (2 x)

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

Solution steps

y^{''} (x) + 9 y = 3 sin (2 x)

Solve linear ODE:

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

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

x \to 4 - lim (2)

y^{^{''}} + 2 y^{^{'}} = 8

y^{^{'}} = - \frac{y}{2000} 4, y (0) = 70

\int_{0}^{\frac{π}{8}} x (sec (2 x))^{2} d x

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

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