What is the solution for 6y^{''}+5y^'-6y=0 ?

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

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6y^{''}+5y^'-6y=0

6 y^{^{''}} + 5 y^{^{'}} - 6 y = 0

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{3 t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{3 t}{2}}

y = c_{1} e^{\frac{2 t}{3}} + c_{2} e^{- \frac{3 t}{2}}

y^{^{''}} + \frac{4}{3} y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - \frac{16}{3}

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

y^{^{'''''}} - 2 y^{^{'''}} + y^{^{'}} = 0

\frac{d ^{2} y}{d x ^{2}} - 36 \frac{d y}{d x} = 0

y^{^{''}} + 9 y = 0

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