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

The solution for y^{''}+y^'-5y=0 is y=c_{1}e^{((-1+sqrt(21))t)/2}+c_{2}e^{((-1-sqrt(21))t)/2}

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

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

y = c_{1} e^{\frac{( - 1 + 21 ) t}{2}} + c_{2} e^{\frac{( - 1 - 21 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 21 ) t}{2}} + c_{2} e^{\frac{( - 1 - 21 ) t}{2}}

y = c_{1} e^{\frac{( - 1 + 21 ) t}{2}} + c_{2} e^{\frac{( - 1 - 21 ) t}{2}}

(y^{^{''}} - 7 y) \frac{1}{9} = 0

2 y^{^{''}} + 10 y^{^{'}} + 18 y = 0

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

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

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = - 5, y^{^{'}} (0) = 14

What is the solution for y^{''}+y^'-5y=0 ?
The solution for y^{''}+y^'-5y=0 is y=c_{1}e^{((-1+sqrt(21))t)/2}+c_{2}e^{((-1-sqrt(21))t)/2}