What is the solution for (d^2y)/(dx^2)-5y=0 ?

The solution for (d^2y)/(dx^2)-5y=0 is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}

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(d^2y)/(dx^2)-5y=0

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0

y = c_{1} e^{5 x} + c_{2} e^{- 5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x}

y^{^{''''}} + 8 y^{^{'''}} + 16 y^{^{''}} = 0

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

y^{^{''}} - 6 y^{^{'}} + 14 y = 0

What is the solution for (d^2y)/(dx^2)-5y=0 ?
The solution for (d^2y)/(dx^2)-5y=0 is y=c_{1}e^{sqrt(5)x}+c_{2}e^{-sqrt(5)x}