What is the solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=-13 ?

The solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=-13 is y=-2e^{2t}+3e^{-3t}

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y^{''}+y^'-6y=0,y(0)=1,y^'(0)=-13

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 13

y = - 2 e^{2 t} + 3 e^{- 3 t}

Solution steps

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

Solve linear ODE:

y = - 2 e^{2 t} + 3 e^{- 3 t}

y = - 2 e^{2 t} + 3 e^{- 3 t}

\int_{0}^{1} x (x - x^{2}) d x

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

x \to - 2 - lim (\frac{x ^{2}}{x ^{2} - 4})

\int \frac{1}{- x ^{2} + 2 x} d x

What is the solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=-13 ?
The solution for y^{''}+y^'-6y=0,y(0)=1,y^'(0)=-13 is y=-2e^{2t}+3e^{-3t}