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

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

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

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

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} = n y (x)

Solve linear ODE:

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

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

4 y^{^{''}} + 9 y^{^{'}} - 9 y = 0

y^{^{''}} + 8 y^{^{'}} + 17 y = 0, y (0) = 0, y^{^{'}} (0) = 7

(d^{3} - 5 d^{2} + 4 d - 20) x = 0

\frac{y ^{^{''}}}{y} = - a^{2}

9 y^{^{''}} - 5 y^{^{'}} = 0, y^{1} (0) = e^{- 7 x}

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