What is the solution for 2y^{''}-3y^'-6y=0 ?

The solution for 2y^{''}-3y^'-6y=0 is y=c_{1}e^{((3+sqrt(57))t)/4}+c_{2}e^{((3-sqrt(57))t)/4}

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2y^{''}-3y^'-6y=0

2 y^{^{''}} - 3 y^{^{'}} - 6 y = 0

y = c_{1} e^{\frac{( 3 + 57 ) t}{4}} + c_{2} e^{\frac{( 3 - 57 ) t}{4}}

Solution steps

2 y^{''} (t) - 3 y^{'} (t) - 6 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 3 + 57 ) t}{4}} + c_{2} e^{\frac{( 3 - 57 ) t}{4}}

y = c_{1} e^{\frac{( 3 + 57 ) t}{4}} + c_{2} e^{\frac{( 3 - 57 ) t}{4}}

9 x^{^{''}} - 12 x^{^{'}} + 4 x = 0, x (0) = 1, x^{^{'}} (0) = - 1

y^{^{''}} + y = 0, y^{^{'}} = 5, y (0) = 9

y^{^{''}} = 7 y^{^{'}} + 4 y

y^{^{''}} + 0.05 y^{^{'}} + 25 y = 0

2 \cdot y^{^{''}} + 4 \cdot y^{^{'}} + 8 y = 0

What is the solution for 2y^{''}-3y^'-6y=0 ?
The solution for 2y^{''}-3y^'-6y=0 is y=c_{1}e^{((3+sqrt(57))t)/4}+c_{2}e^{((3-sqrt(57))t)/4}