What is the solution for 2y^{''}-5y^'-6y=0 ?

The solution for 2y^{''}-5y^'-6y=0 is y=c_{1}e^{((5+sqrt(73))t)/4}+c_{2}e^{((5-sqrt(73))t)/4}

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2y^{''}-5y^'-6y=0

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

y = c_{1} e^{\frac{( 5 + 73 ) t}{4}} + c_{2} e^{\frac{( 5 - 73 ) t}{4}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 5 + 73 ) t}{4}} + c_{2} e^{\frac{( 5 - 73 ) t}{4}}

y = c_{1} e^{\frac{( 5 + 73 ) t}{4}} + c_{2} e^{\frac{( 5 - 73 ) t}{4}}

8 y^{^{''}} - 2 y^{^{'}} - 3 y = 0

y^{^{''}} + 2 y^{^{'}} - 63 y = 0, y (0) = a, y^{^{'}} (0) = 36

(D^{3} - 4 D^{2} + 4 D) y = 0

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = 7

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} = 0

What is the solution for 2y^{''}-5y^'-6y=0 ?
The solution for 2y^{''}-5y^'-6y=0 is y=c_{1}e^{((5+sqrt(73))t)/4}+c_{2}e^{((5-sqrt(73))t)/4}