What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+29y=0 ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)+29y=0 is y=e^{-2x}(c_{1}cos(5x)+c_{2}sin(5x))

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(d^2y)/(dx^2)+4(dy)/(dx)+29y=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 29 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} + 29 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))

x^{^{''}} + 2 x^{^{'}} + 26 x = 0

\frac{d ^{2} f}{d x ^{2}} + k^{2} f (x) = 0

2 y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

x^{^{''}} + 8 x^{^{'}} = 0, x (0) = - 3, x^{^{'}} (0) = 5

y^{^{''}} - 6 y^{^{''}} + 8 y = 0

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+29y=0 ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)+29y=0 is y=e^{-2x}(c_{1}cos(5x)+c_{2}sin(5x))