What is the solution for 9y^{''}-6y^'-y=0 ?

The solution for 9y^{''}-6y^'-y=0 is y=c_{1}e^{((1+sqrt(2))t)/3}+c_{2}e^{((1-sqrt(2))t)/3}

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9y^{''}-6y^'-y=0

9 y^{^{''}} - 6 y^{^{'}} - y = 0

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''''}} + 4 y = 0

y^{^{''}} + y^{^{'}} - y = 0, y (- 4) = 7, y^{^{'}} (- 4) = 1

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

y^{^{''''''''}} + 8 y^{^{''''}} + 16 y = 0

y^{^{''}} + y = 0, y (\frac{π}{3}) = 6, y^{^{'}} (\frac{π}{3}) = - 12

What is the solution for 9y^{''}-6y^'-y=0 ?
The solution for 9y^{''}-6y^'-y=0 is y=c_{1}e^{((1+sqrt(2))t)/3}+c_{2}e^{((1-sqrt(2))t)/3}