What is the solution for (d^2y)/(dx^2)=(4y) ?

The solution for (d^2y)/(dx^2)=(4y) is y=c_{1}e^{2x}+c_{2}e^{-2x}

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(d^2y)/(dx^2)=(4y)

\frac{d ^{2} y}{d x ^{2}} = (4 y)

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} = (4 y)

Solve linear ODE:

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

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

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 3, y^{^{'}} (0) = 1

y^{^{'''}} + 3 y^{^{''}} + 4 y^{^{'}} + 12 y = 0

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

y^{^{''}} + 4 y = 0, y (\frac{π}{4}) = - 2

x^{^{''}} + \frac{1}{4} x^{^{'}} + x = 0

What is the solution for (d^2y)/(dx^2)=(4y) ?
The solution for (d^2y)/(dx^2)=(4y) is y=c_{1}e^{2x}+c_{2}e^{-2x}