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

The solution for y^{''}-9y^'+6y=0 is y=c_{1}e^{((9+sqrt(57))t)/2}+c_{2}e^{((9-sqrt(57))t)/2}

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

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

y = c_{1} e^{\frac{( 9 + 57 ) t}{2}} + c_{2} e^{\frac{( 9 - 57 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 9 + 57 ) t}{2}} + c_{2} e^{\frac{( 9 - 57 ) t}{2}}

y = c_{1} e^{\frac{( 9 + 57 ) t}{2}} + c_{2} e^{\frac{( 9 - 57 ) t}{2}}

16 y^{^{''}} + 522.67 y = 0

\frac{d ^{2} y}{d t ^{2}} + 64 y = 0

y^{^{'''}} + 6 y^{^{''}} - 37 y^{^{'}} - 90 y = 0

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

u, \frac{d ^{2} u}{d x ^{2}} = a u (x)

What is the solution for y^{''}-9y^'+6y=0 ?
The solution for y^{''}-9y^'+6y=0 is y=c_{1}e^{((9+sqrt(57))t)/2}+c_{2}e^{((9-sqrt(57))t)/2}