What is the solution for 2y^{''}+6y^'-(9y)/2 =0 ?

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

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2y^{''}+6y^'-(9y)/2 =0

2 y^{^{''}} + 6 y^{^{'}} - \frac{9 y}{2} = 0

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

Solution steps

2 y^{''} (t) + 6 y^{'} (t) - \frac{9 y}{2} = 0

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} + 4 y = 0, y = 0

9 y^{^{''}} + 4 y^{^{'}} = - 5 y

y^{^{''}} - \frac{3}{2} y^{^{'}} + y = 0

77 y^{^{''''}} + 39 y^{^{''}} + 4 y = 0

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