What is the solution for (d^2y)/(dx^2)+6*((dy)/(dx))+8*y=0 ?

The solution for (d^2y)/(dx^2)+6*((dy)/(dx))+8*y=0 is y=c_{1}e^{-2x}+c_{2}e^{-4x}

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(d^2y)/(dx^2)+6((dy)/(dx))+8y=0

\frac{d ^{2} y}{d x ^{2}} + 6 \cdot (\frac{d y}{d x}) + 8 \cdot y = 0

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 6 \cdot (\frac{d y}{d x}) + 8 \cdot y = 0

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 4 x}

y^{^{''}} - 9 y = 0, y^{^{'}} (0) = 10

x^{^{''}} + 3 x^{^{'}} = 0

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

y^{^{''}} - 6 y^{^{'}} - 5 y = 0

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

What is the solution for (d^2y)/(dx^2)+6*((dy)/(dx))+8*y=0 ?
The solution for (d^2y)/(dx^2)+6*((dy)/(dx))+8*y=0 is y=c_{1}e^{-2x}+c_{2}e^{-4x}