What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)-20y=0 ?

The solution for (d^2y)/(dx^2)+8(dy)/(dx)-20y=0 is y=c_{1}e^{2x}+c_{2}e^{-10x}

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(d^2y)/(dx^2)+8(dy)/(dx)-20y=0

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} - 20 y = 0

y = c_{1} e^{2 x} + c_{2} e^{- 10 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} - 20 y = 0

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 10 x}

y = c_{1} e^{2 x} + c_{2} e^{- 10 x}

y^{^{''}} + 2 y^{^{'}} + y = 0, y (0) = 5, y (0) = - 3

y^{^{'''}} + 6 y^{^{''}} - 19 y^{^{'}} - 24 y = 0

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

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

25 y^{^{''}} - 30 y^{^{'}} + 9 y = 0, y^{1} (0) = e^{3} \frac{x}{5}

What is the solution for (d^2y)/(dx^2)+8(dy)/(dx)-20y=0 ?
The solution for (d^2y)/(dx^2)+8(dy)/(dx)-20y=0 is y=c_{1}e^{2x}+c_{2}e^{-10x}