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

The solution for 2y^{''}+9y^'-y=0 is y=c_{1}e^{((-9+sqrt(89))t)/4}+c_{2}e^{((-9-sqrt(89))t)/4}

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2y^{''}+9y^'-y=0

2 y^{^{''}} + 9 y^{^{'}} - y = 0

y = c_{1} e^{\frac{( - 9 + 89 ) t}{4}} + c_{2} e^{\frac{( - 9 - 89 ) t}{4}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 89 ) t}{4}} + c_{2} e^{\frac{( - 9 - 89 ) t}{4}}

y = c_{1} e^{\frac{( - 9 + 89 ) t}{4}} + c_{2} e^{\frac{( - 9 - 89 ) t}{4}}

y^{^{''}} + \frac{1}{4} y^{^{'}} + 2 y = 0

y^{^{''}} = 3 y^{^{'}} + 5 y, y (0) = 8

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

u^{^{''}} + 23 H (t) = 0

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = 0, y (0) = 2

What is the solution for 2y^{''}+9y^'-y=0 ?
The solution for 2y^{''}+9y^'-y=0 is y=c_{1}e^{((-9+sqrt(89))t)/4}+c_{2}e^{((-9-sqrt(89))t)/4}