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

The solution for (d^2y)/(dx^2)=k^2y is y=c_{1}e^{kx}+c_{2}e^{-kx}

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(d^2y)/(dx^2)=k^2y

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

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

Solution steps

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

Solve linear ODE:

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

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

9 y^{^{''}} + 17 y^{^{'}} - 2 y = 0

y^{^{''}} + 4 y^{^{'}} + 40 y = 0

y^{^{'''}} - 12 y^{^{''}} + 48 y^{^{'}} - 64 y = 0

x^{^{''}} + 4 x^{^{'}} + 20 x = 0

y^{^{''}} + 3 y^{^{'}} = 0

What is the solution for (d^2y)/(dx^2)=k^2y ?
The solution for (d^2y)/(dx^2)=k^2y is y=c_{1}e^{kx}+c_{2}e^{-kx}