What is the solution for y^{''}-9y^'+7y=0 ?

The solution for y^{''}-9y^'+7y=0 is y=c_{1}e^{((9+sqrt(53))t)/2}+c_{2}e^{((9-sqrt(53))t)/2}

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y^{''}-9y^'+7y=0

y^{^{''}} - 9 y^{^{'}} + 7 y = 0

y = c_{1} e^{\frac{( 9 + 53 ) t}{2}} + c_{2} e^{\frac{( 9 - 53 ) t}{2}}

Solution steps

y^{''} (t) - 9 y^{'} (t) + 7 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 9 + 53 ) t}{2}} + c_{2} e^{\frac{( 9 - 53 ) t}{2}}

y = c_{1} e^{\frac{( 9 + 53 ) t}{2}} + c_{2} e^{\frac{( 9 - 53 ) t}{2}}

3 y^{^{'''}} + 5 y^{^{''}} = 0

5 y^{^{''}} + 5 y^{^{'}} + 10 y = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 2, y^{^{'}} (0) = 1

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

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 3, y^{^{'}} (0) = - 5

What is the solution for y^{''}-9y^'+7y=0 ?
The solution for y^{''}-9y^'+7y=0 is y=c_{1}e^{((9+sqrt(53))t)/2}+c_{2}e^{((9-sqrt(53))t)/2}