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

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

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

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

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

Solution steps

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

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}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 0

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 0

2 y^{^{''''}} + 11 y^{^{'''}} + 18 y^{^{''}} + 4 y^{^{'}} - 8 y = 0

3 y^{^{''}} - 5 y^{^{'}} + 2 y = 0

u^{^{'''}} + u^{^{''}} - 2 H (t) = 0

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