What is the solution for y^{''}-y=0,y(0)=0,y^'(0)=5 ?

The solution for y^{''}-y=0,y(0)=0,y^'(0)=5 is y= 5/2 e^t-5/2 e^{-t}

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

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

y = \frac{5}{2} e^{t} - \frac{5}{2} e^{- t}

Solution steps

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

Solve linear ODE:

y = \frac{5}{2} e^{t} - \frac{5}{2} e^{- t}

y = \frac{5}{2} e^{t} - \frac{5}{2} e^{- t}

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (π) = 1, y (0) = 1

\frac{1}{8} y^{^{''}} + y^{^{'}} + 2 y = 0, y (0) = - 1, y^{^{'}} (0) = 12

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 2, y^{^{'}} (0) = - 5

x^{^{''}} + a x^{^{'}} = 0

y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} - 20 y = 0

What is the solution for y^{''}-y=0,y(0)=0,y^'(0)=5 ?
The solution for y^{''}-y=0,y(0)=0,y^'(0)=5 is y= 5/2 e^t-5/2 e^{-t}