What is the solution for y^{''}-4y=0,y(0)=0 ?

The solution for y^{''}-4y=0,y(0)=0 is y=-c_{2}e^{2t}+c_{2}e^{-2t}

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y^{''}-4y=0,y(0)=0

y^{^{''}} - 4 y = 0, y (0) = 0

y = - c_{2} e^{2 t} + c_{2} e^{- 2 t}

Solution steps

y^{''} (t) - 4 y = 0

Solve linear ODE:

y = - c_{2} e^{2 t} + c_{2} e^{- 2 t}

y = - c_{2} e^{2 t} + c_{2} e^{- 2 t}

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

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

x^{^{''}} + 2 x^{^{'}} + 1^{2} x = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 0, y (0) = 5, y^{^{'}} (0) = 10

x^{^{''}} - 2 x^{^{'}} + 3 x = 0

What is the solution for y^{''}-4y=0,y(0)=0 ?
The solution for y^{''}-4y=0,y(0)=0 is y=-c_{2}e^{2t}+c_{2}e^{-2t}