What is the solution for (d^2y)/(dx^2)+9y=5sin(4x) ?

The solution for (d^2y)/(dx^2)+9y=5sin(4x) is y=c_{1}cos(3x)+c_{2}sin(3x)-5/7 sin(4x)

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(d^2y)/(dx^2)+9y=5sin(4x)

\frac{d ^{2} y}{d x ^{2}} + 9 y = 5 sin (4 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{5}{7} sin (4 x)

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 y = 5 sin (4 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{5}{7} sin (4 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{5}{7} sin (4 x)

y^{^{''}} + y = cos (t), y (0) = 1, y^{^{'}} (0) = - 3

2 y^{^{''}} + 27 y = e^{t} - e^{- t}, y^{t} (0) = 2, y (0) = 0

y^{^{''}} - \frac{2}{5} y = - x^{2}

3 y^{^{'}} + 2 y^{^{''}} = - cos (3.14 \cdot \frac{t}{0.2})

3 y^{^{''}} - 2 y^{^{'}} + 2 y = x + 5

What is the solution for (d^2y)/(dx^2)+9y=5sin(4x) ?
The solution for (d^2y)/(dx^2)+9y=5sin(4x) is y=c_{1}cos(3x)+c_{2}sin(3x)-5/7 sin(4x)