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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

2 y^{^{''}} - y^{^{'}} - 3 y = 0, y (2) = 5, y^{^{'}} (2) = 0

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

y^{^{''}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 5

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

625 y^{^{''''}} = 81 y

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