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

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

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

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

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - cy (x) = 0

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + 49 y = 0

y^{^{''''}} - 32 y^{^{'''}} + 256 y^{^{''}} = 0

y^{^{''''''}} - 729 y = 0

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

x^{^{''}} + 4 x^{^{'}} + 3 x = 0

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