What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+5y=0 ?

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

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(d^2y)/(dx^2)+4(dy)/(dx)+5y=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 0

Solve linear ODE:

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

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

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