What is the solution for (d^2y)/(dx^2)+7(dy)/(dx)-8y=0 ?

The solution for (d^2y)/(dx^2)+7(dy)/(dx)-8y=0 is y=c_{1}e^x+c_{2}e^{-8x}

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(d^2y)/(dx^2)+7(dy)/(dx)-8y=0

\frac{d ^{2} y}{d x ^{2}} + 7 \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}} + 7 \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}

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

y^{^{''}} - 16 y^{^{'}} + 113 y = 0

y^{^{'''}} - 9 y^{^{''}} + 8 y^{^{'}} = 0

\frac{d ^{4} x}{d t ^{4}} - x = 0

y^{^{''}} + 2 y^{^{'}} + 17 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for (d^2y)/(dx^2)+7(dy)/(dx)-8y=0 ?
The solution for (d^2y)/(dx^2)+7(dy)/(dx)-8y=0 is y=c_{1}e^x+c_{2}e^{-8x}