What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+9y=0 ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)+9y=0 is y=e^{-2x}(c_{1}cos(sqrt(5)x)+c_{2}sin(sqrt(5)x))

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(d^2y)/(dx^2)+4(dy)/(dx)+9y=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 9 y = 0

y = e^{- 2 x} (c_{1} cos (5 x) + c_{2} sin (5 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 9 y = 0

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (5 x) + c_{2} sin (5 x))

y = e^{- 2 x} (c_{1} cos (5 x) + c_{2} sin (5 x))

y^{^{''}} + 20 y^{^{'}} + 100 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (- 1) = 5

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y^{0} = 1, y^{^{'}} 0 = 0

y^{^{''}} - 2 π y^{^{'}} + π^{2} y = 0

y^{^{''}} - 2 y - 3 y = 0

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+9y=0 ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)+9y=0 is y=e^{-2x}(c_{1}cos(sqrt(5)x)+c_{2}sin(sqrt(5)x))