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}

\frac{d}{d x} (ln (e^{4 x}))

\frac{d}{d y} (y cos (x - y))

y = x^{3} + 6

\frac{s}{( s + 1 ) ( s + 2 )}

\frac{2}{s ^{2} + 6 s + 13}

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}