What is the solution for (d^2y)/(dx^2)=3y ?

The solution for (d^2y)/(dx^2)=3y is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}

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(d^2y)/(dx^2)=3y

\frac{d ^{2} y}{d x ^{2}} = 3 y

y = c_{1} e^{3 x} + c_{2} e^{- 3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} = 3 y

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x}

y^{^{''}} + 3 y^{^{'}} - 7 y = 0

y^{^{''}} + 1960 y = 0, y (0) = 0.015, y^{^{'}} (0) = 0

y^{^{''}} - 4 y + 7 y = 0

y^{^{''}} + 100 y = 0, y (π) = 5, y (0) = 2

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = 7

What is the solution for (d^2y)/(dx^2)=3y ?
The solution for (d^2y)/(dx^2)=3y is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}