What is the solution for y^{''}-9y^'+5y=0 ?

The solution for y^{''}-9y^'+5y=0 is y=c_{1}e^{((9+sqrt(61))t)/2}+c_{2}e^{((9-sqrt(61))t)/2}

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y^{''}-9y^'+5y=0

y^{^{''}} - 9 y^{^{'}} + 5 y = 0

y = c_{1} e^{\frac{( 9 + 61 ) t}{2}} + c_{2} e^{\frac{( 9 - 61 ) t}{2}}

Solution steps

y^{''} (t) - 9 y^{'} (t) + 5 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 9 + 61 ) t}{2}} + c_{2} e^{\frac{( 9 - 61 ) t}{2}}

y = c_{1} e^{\frac{( 9 + 61 ) t}{2}} + c_{2} e^{\frac{( 9 - 61 ) t}{2}}

2 y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 0

4 y^{^{''}} + 4 y^{^{'}} - 3 y = 0

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

x^{^{''}} - 2 x^{^{'}} = 0

y^{^{''}} - 25 y^{^{'}} + 144 y = 0, y (0) = 2

What is the solution for y^{''}-9y^'+5y=0 ?
The solution for y^{''}-9y^'+5y=0 is y=c_{1}e^{((9+sqrt(61))t)/2}+c_{2}e^{((9-sqrt(61))t)/2}