What is the solution for 4(d^2y)/(dx^2)+9y=15 ?

The solution for 4(d^2y)/(dx^2)+9y=15 is y=c_{1}cos((3x)/2)+c_{2}sin((3x)/2)+5/3

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4(d^2y)/(dx^2)+9y=15

4 \frac{d ^{2} y}{d x ^{2}} + 9 y = 15

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

Solution steps

4 \frac{d ^{2} y}{d x ^{2}} + 9 y = 15

Solve linear ODE:

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

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

y^{^{''}} - y = sin (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 4 x + 5

3 x^{^{''}} + 30 x^{^{'}} + 125 x = 350

y^{^{''}} + y = t^{2} + 1

y^{^{''}} + 4 y^{^{'}} + 4 y = 5 e^{3 t}

What is the solution for 4(d^2y)/(dx^2)+9y=15 ?
The solution for 4(d^2y)/(dx^2)+9y=15 is y=c_{1}cos((3x)/2)+c_{2}sin((3x)/2)+5/3