What is the solution for y^{''}+5y^'-6y=0,y(0)=2,y^'(0)=-1 ?

The solution for y^{''}+5y^'-6y=0,y(0)=2,y^'(0)=-1 is y=(2-3/7)e^t+3/7 e^{-6t}

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y^{''}+5y^'-6y=0,y(0)=2,y^'(0)=-1

y^{^{''}} + 5 y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

y = (2 - \frac{3}{7}) e^{t} + \frac{3}{7} e^{- 6 t}

Solution steps

y^{''} (t) + 5 y^{'} (t) - 6 y = 0

Solve linear ODE:

y = (2 - \frac{3}{7}) e^{t} + \frac{3}{7} e^{- 6 t}

y = (2 - \frac{3}{7}) e^{t} + \frac{3}{7} e^{- 6 t}

\int \frac{8}{x ^{2} - 2 x} d x

x y^{2} d x + e^{x} d y = 0

\frac{2 s}{( s ^{2} + 1 ) ^{2}}

\int sin (\frac{1}{2 x}) d x

y = 16 x

What is the solution for y^{''}+5y^'-6y=0,y(0)=2,y^'(0)=-1 ?
The solution for y^{''}+5y^'-6y=0,y(0)=2,y^'(0)=-1 is y=(2-3/7)e^t+3/7 e^{-6t}