What is the solution for y^{''}+y^'-10y=0 ?

The solution for y^{''}+y^'-10y=0 is y=c_{1}e^{((-1+sqrt(41))t)/2}+c_{2}e^{((-1-sqrt(41))t)/2}

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

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

y = c_{1} e^{\frac{( - 1 + 41 ) t}{2}} + c_{2} e^{\frac{( - 1 - 41 ) t}{2}}

Solution steps

y^{''} (t) + y^{'} (t) - 10 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 41 ) t}{2}} + c_{2} e^{\frac{( - 1 - 41 ) t}{2}}

y = c_{1} e^{\frac{( - 1 + 41 ) t}{2}} + c_{2} e^{\frac{( - 1 - 41 ) t}{2}}

y^{^{''}} - 2 y + 5 y = 0

y^{^{''}} - 12 y^{^{'}} + 27 y = 0

y^{^{'''}} - 4 y^{^{''}} + 8 y^{^{'}} = 0

y^{^{''}} - (\frac{8}{3}) y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = - 73

6 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

What is the solution for y^{''}+y^'-10y=0 ?
The solution for y^{''}+y^'-10y=0 is y=c_{1}e^{((-1+sqrt(41))t)/2}+c_{2}e^{((-1-sqrt(41))t)/2}