What is the solution for ((d^2y)/(dx^2))-4y=0 ?

The solution for ((d^2y)/(dx^2))-4y=0 is y=c_{1}e^{2x}+c_{2}e^{-2x}

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((d^2y)/(dx^2))-4y=0

(\frac{d ^{2} y}{d x ^{2}}) - 4 y = 0

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

Solution steps

(\frac{d ^{2} y}{d x ^{2}}) - 4 y = 0

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

x^{^{''}} + 4 x = 0, x (0) = 1, x^{^{'}} (0) = - 2

y^{^{''}} + 12 y^{^{'}} + 37 y = 4 y

y^{^{''}} - y^{^{'}} - 12 y = 0, y (1) = 0 y^{^{'}} (1)

y^{^{'''}} - 5 y^{^{''}} - 4 y^{^{'}} + 20 y = 0

What is the solution for ((d^2y)/(dx^2))-4y=0 ?
The solution for ((d^2y)/(dx^2))-4y=0 is y=c_{1}e^{2x}+c_{2}e^{-2x}