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

The solution for -5y^'+2y^{''}-y^'-6y=0 is y=c_{1}e^{((3+sqrt(21))t)/2}+c_{2}e^{((3-sqrt(21))t)/2}

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

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

y = c_{1} e^{\frac{( 3 + 21 ) t}{2}} + c_{2} e^{\frac{( 3 - 21 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 3 + 21 ) t}{2}} + c_{2} e^{\frac{( 3 - 21 ) t}{2}}

y = c_{1} e^{\frac{( 3 + 21 ) t}{2}} + c_{2} e^{\frac{( 3 - 21 ) t}{2}}

121 y^{^{''}} - 154 y^{^{'}} + 74 y = 0

\frac{d ^{2} y}{d x ^{2}} = - a^{2} y

y^{^{''}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 2

49 y^{^{''}} - 126 y^{^{'}} + 117 y = 0, y (4) = 2, y^{^{'}} (4) = 2

y^{^{''}} - 3 y^{^{'}} = 0, y (0) = 6 - 6 e^{3}, y (1) = 0

What is the solution for -5y^'+2y^{''}-y^'-6y=0 ?
The solution for -5y^'+2y^{''}-y^'-6y=0 is y=c_{1}e^{((3+sqrt(21))t)/2}+c_{2}e^{((3-sqrt(21))t)/2}