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

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

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linear (d^2y)/(dx^2)=16y

linear

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

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

Solution steps

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

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^{^{''}} + 12 y^{^{'}} + 34 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{'''}} - 13 y^{^{''}} + 36 y^{^{'}} = 0

y^{^{''}} + 4 y^{^{'}} - 32 y = 0, y (0) = - 3, y^{^{'}} (0) = - 12

10 y^{^{''}} + 6 y^{^{'}} + y = 0

u^{^{''}} + 14 H (t) = 0

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