What is the solution for y^{''}-6y=0,y(0)=13,y^'(0)=0 ?

The solution for y^{''}-6y=0,y(0)=13,y^'(0)=0 is y=(13-13/2)e^{sqrt(6)t}+13/2 e^{-sqrt(6)t}

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

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

y = (13 - \frac{13}{2}) e^{6 t} + \frac{13}{2} e^{- 6 t}

Solution steps

y^{''} (t) - 6 y = 0

Solve linear ODE:

y = (13 - \frac{13}{2}) e^{6 t} + \frac{13}{2} e^{- 6 t}

y = (13 - \frac{13}{2}) e^{6 t} + \frac{13}{2} e^{- 6 t}

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (1) - 2 y = 0

y^{^{'''}} - 15 y^{^{''}} + 62 y^{^{'}} - 72 y = 0

y^{^{''}} + 2 y^{^{'}} = - y

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

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 2

What is the solution for y^{''}-6y=0,y(0)=13,y^'(0)=0 ?
The solution for y^{''}-6y=0,y(0)=13,y^'(0)=0 is y=(13-13/2)e^{sqrt(6)t}+13/2 e^{-sqrt(6)t}