What is the solution for y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2 ?

The solution for y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2 is y=(2-12/11)e^{5t}+12/11 e^{-6t}

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y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2

y^{^{''}} + y^{^{'}} - 30 y = 0, y (0) = 2, y^{^{'}} (0) = - 2

y = (2 - \frac{12}{11}) e^{5 t} + \frac{12}{11} e^{- 6 t}

Solution steps

y^{''} (t) + y^{'} (t) - 30 y = 0

Solve linear ODE:

y = (2 - \frac{12}{11}) e^{5 t} + \frac{12}{11} e^{- 6 t}

y = (2 - \frac{12}{11}) e^{5 t} + \frac{12}{11} e^{- 6 t}

What is the solution for y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2 ?
The solution for y^{''}+y^'-30y=0,y(0)=2,y^'(0)=-2 is y=(2-12/11)e^{5t}+12/11 e^{-6t}