What is the solution for y^{''}-16y=0,y(0)=4,y^'(0)=-4 ?

The solution for y^{''}-16y=0,y(0)=4,y^'(0)=-4 is y=(4-5/2)e^{4t}+5/2 e^{-4t}

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y^{''}-16y=0,y(0)=4,y^'(0)=-4

y^{^{''}} - 16 y = 0, y (0) = 4, y^{^{'}} (0) = - 4

y = (4 - \frac{5}{2}) e^{4 t} + \frac{5}{2} e^{- 4 t}

Solution steps

y^{''} (t) - 16 y = 0

Solve linear ODE:

y = (4 - \frac{5}{2}) e^{4 t} + \frac{5}{2} e^{- 4 t}

y = (4 - \frac{5}{2}) e^{4 t} + \frac{5}{2} e^{- 4 t}

What is the solution for y^{''}-16y=0,y(0)=4,y^'(0)=-4 ?
The solution for y^{''}-16y=0,y(0)=4,y^'(0)=-4 is y=(4-5/2)e^{4t}+5/2 e^{-4t}