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

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

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

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

y = (1 - \frac{3}{5}) e^{3 t} + \frac{3}{5} e^{- 2 t}

Solution steps

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

Solve linear ODE:

y = (1 - \frac{3}{5}) e^{3 t} + \frac{3}{5} e^{- 2 t}

y = (1 - \frac{3}{5}) e^{3 t} + \frac{3}{5} e^{- 2 t}

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

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