What is the solution for (d^2y)/(dx^2)+11(dy)/(dx)+24y=0 ?

The solution for (d^2y)/(dx^2)+11(dy)/(dx)+24y=0 is y=c_{1}e^{-3x}+c_{2}e^{-8x}

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(d^2y)/(dx^2)+11(dy)/(dx)+24y=0

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 24 y = 0

y = c_{1} e^{- 3 x} + c_{2} e^{- 8 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 24 y = 0

Solve linear ODE:

y = c_{1} e^{- 3 x} + c_{2} e^{- 8 x}

y = c_{1} e^{- 3 x} + c_{2} e^{- 8 x}

x^{^{''}} + 2 x^{^{'}} + 8 x = 0

y^{^{''}} - 15 y^{^{'}} + 50 y = 0

y^{^{''}} + 4 y = 0, y^{^{'}} (0) = 0, y (0) = 0

0.701 x^{^{''}} + 27.4667 x = 0

\frac{1}{8} x^{^{''}} + x^{^{'}} + 2 x = 0

What is the solution for (d^2y)/(dx^2)+11(dy)/(dx)+24y=0 ?
The solution for (d^2y)/(dx^2)+11(dy)/(dx)+24y=0 is y=c_{1}e^{-3x}+c_{2}e^{-8x}