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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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