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

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

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

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

y = (4 - c_{2}) e^{4 t} + c_{2} e^{- 4 t}

Solution steps

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

Solve linear ODE:

y = (4 - c_{2}) e^{4 t} + c_{2} e^{- 4 t}

y = (4 - c_{2}) e^{4 t} + c_{2} e^{- 4 t}

21 y^{^{''''}} + 187 y^{^{''}} + 400 y = 0

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

y^{^{''}} + 6 y^{^{'}} + 18 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

x^{^{''}} - 8 x^{^{'}} + 16 x = 0

\frac{d ^{3} x}{d t ^{3}} - \frac{d ^{2} x}{d t ^{2}} - 4 x = 0

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