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

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

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(d^2y)/(dx^2)+k^2*y^'=0

\frac{d ^{2} y}{d x ^{2}} + k^{2} \cdot y^{^{'}} = 0

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

Solution steps

y^{''} (x) + k^{2} \cdot y^{'} (x) = 0

Solve linear ODE:

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

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

4 y^{^{''}} + 4 y^{^{'}} + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 35 y = 0

y^{^{''}} + y^{^{'}} + 3.25 y = 0

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

16 y^{^{''}} + 9 y = 0

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