What is the solution for (d^2y)/(dx^2)-16y=0 ?

The solution for (d^2y)/(dx^2)-16y=0 is y=c_{1}e^{4x}+c_{2}e^{-4x}

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(d^2y)/(dx^2)-16y=0

\frac{d ^{2} y}{d x ^{2}} - 16 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 16 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 1, y^{^{'}} (0) = 1

2 x^{^{''}} + 3 x^{^{'}} + 7 x = 0

y^{^{''}} = 3 y^{^{'}} + 5 y

3 y^{^{''}} + 38 y^{^{'}} + 80 y = 0, y (0) = 3, y^{^{'}} (0) = 7

a x^{^{''}} + b x^{^{'}} + c x = 0

What is the solution for (d^2y)/(dx^2)-16y=0 ?
The solution for (d^2y)/(dx^2)-16y=0 is y=c_{1}e^{4x}+c_{2}e^{-4x}