What is the solution for y^{''}+9y^'-20y=0 ?

The solution for y^{''}+9y^'-20y=0 is y=c_{1}e^{((-9+sqrt(161))t)/2}+c_{2}e^{((-9-sqrt(161))t)/2}

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y^{''}+9y^'-20y=0

y^{^{''}} + 9 y^{^{'}} - 20 y = 0

y = c_{1} e^{\frac{( - 9 + 161 ) t}{2}} + c_{2} e^{\frac{( - 9 - 161 ) t}{2}}

Solution steps

y^{''} (t) + 9 y^{'} (t) - 20 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 9 + 161 ) t}{2}} + c_{2} e^{\frac{( - 9 - 161 ) t}{2}}

y = c_{1} e^{\frac{( - 9 + 161 ) t}{2}} + c_{2} e^{\frac{( - 9 - 161 ) t}{2}}

y^{^{''}} - 20 y^{^{'}} + 64 y = 0

f^{^{''}} (t) - c f (t) = 0

y^{^{'''}} + 8 y^{^{''}} + 25 y^{^{'}} = 0

4 y^{^{''}} - 2 y^{^{'}} - 2 y = 0, y (0) = 3, y^{^{'}} (0) = 1

x^{^{'''}} - 10 x^{^{''}} + 37 x^{^{'}} - 52 x = 0

What is the solution for y^{''}+9y^'-20y=0 ?
The solution for y^{''}+9y^'-20y=0 is y=c_{1}e^{((-9+sqrt(161))t)/2}+c_{2}e^{((-9-sqrt(161))t)/2}