What is the solution for y^{''}-y^'-6y=0,y(0)=-1,y^'(0)=4 ?

The solution for y^{''}-y^'-6y=0,y(0)=-1,y^'(0)=4 is y=(-1+7/5)e^{3t}-7/5 e^{-2t}

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y^{''}-y^'-6y=0,y(0)=-1,y^'(0)=4

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = - 1, y^{^{'}} (0) = 4

y = (- 1 + \frac{7}{5}) e^{3 t} - \frac{7}{5} e^{- 2 t}

Solution steps

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

Solve linear ODE:

y = (- 1 + \frac{7}{5}) e^{3 t} - \frac{7}{5} e^{- 2 t}

y = (- 1 + \frac{7}{5}) e^{3 t} - \frac{7}{5} e^{- 2 t}

\int e^{2 - 5 x} d x

x \to 2 + lim (\frac{1}{x ^{2} - 5 x + 6})

2 y^{^{''}} + (a + 1) y = 0

\int {\frac{3 - x}{x ^{2} + 1} + x ln (x^{2})} d x

y = 1 + 3 x^{2} (ln (x^{2}))

What is the solution for y^{''}-y^'-6y=0,y(0)=-1,y^'(0)=4 ?
The solution for y^{''}-y^'-6y=0,y(0)=-1,y^'(0)=4 is y=(-1+7/5)e^{3t}-7/5 e^{-2t}