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

The solution for (d^2y)/(dx^2)+6(dy)/(dx)+8y=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 \frac{d y}{d x} + 8 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 8 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}

6 y^{^{''}} + 35 y = 0, y (0) = 3, y^{^{'}} (0) = 8

16 y^{^{''''}} = y

3 y^{^{''}} + 10 y^{^{'}} - 8 y = 0

y^{^{'''}} + 4 y^{^{''}} - 128 y = 0

y^{^{''''}} - 2 y^{^{'''}} + 4 y^{^{''}} + 2 y^{^{'}} - 5 y = 0

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