What is the solution for (d^2y)/(dx^2)+4y=2sin(3x) ?

The solution for (d^2y)/(dx^2)+4y=2sin(3x) is y=c_{1}cos(2x)+c_{2}sin(2x)-2/5 sin(3x)

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(d^2y)/(dx^2)+4y=2sin(3x)

\frac{d ^{2} y}{d x ^{2}} + 4 y = 2 sin (3 x)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = 2 sin (3 x)

Solve linear ODE:

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

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

y^{^{'}} = k + b cos (2 π t)

\frac{d}{d x} (2 x^{3} + 5)

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

x \to 0 lim (\frac{x}{∣ x ∣} + 2)

sin (2 θ)

What is the solution for (d^2y)/(dx^2)+4y=2sin(3x) ?
The solution for (d^2y)/(dx^2)+4y=2sin(3x) is y=c_{1}cos(2x)+c_{2}sin(2x)-2/5 sin(3x)