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}

(2 x + 1)^{^{'}}

y^{^{'}} = (y + 2 x)^{2}, y (0) = 3

4 x^{4} + 3 x^{3} + 2 x^{2} + x + 11

\frac{d}{d x} (\frac{- 1}{x})

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{2 + x})

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}