What is the solution for (d^2y)/(dx^2)+9(dy)/(dx)+8y=0 ?

The solution for (d^2y)/(dx^2)+9(dy)/(dx)+8y=0 is y=c_{1}e^{-x}+c_{2}e^{-8x}

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(d^2y)/(dx^2)+9(dy)/(dx)+8y=0

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 8 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 \frac{d y}{d x} + 8 y = 0

Solve linear ODE:

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

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

2 y^{^{''}} + 12 y^{^{'}} + 68 y = 0, y (0) = 3, y^{^{'}} (0) = 0

x^{^{'''}} + 7 x^{^{''}} - 5 x^{^{'}} - 75 x = 0

y^{^{''}} - 14 y^{^{'}} + 5 y = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} - 17 y = 0

What is the solution for (d^2y)/(dx^2)+9(dy)/(dx)+8y=0 ?
The solution for (d^2y)/(dx^2)+9(dy)/(dx)+8y=0 is y=c_{1}e^{-x}+c_{2}e^{-8x}