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

The solution for y^{''}-10y^'+αy=0 is y=c_{1}e^{(5+sqrt(-α+25))t}+c_{2}e^{(5-sqrt(-α+25))t}

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y^{''}-10y^'+αy=0

y^{^{''}} - 10 y^{^{'}} + α y = 0

y = c_{1} e^{(5 + - α + 25) t} + c_{2} e^{(5 - - α + 25) t}

Solution steps

y^{''} (t) - 10 y^{'} (t) + α y = 0

Solve linear ODE:

y = c_{1} e^{(5 + - α + 25) t} + c_{2} e^{(5 - - α + 25) t}

y = c_{1} e^{(5 + - α + 25) t} + c_{2} e^{(5 - - α + 25) t}

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

y^{^{''}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

y^{^{''''}} - 40 y^{^{'''}} + 400 y^{^{''}} = 0

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 24 y = 0

x^{^{''}} + 2 x^{^{'}} + 8 x = 0

What is the solution for y^{''}-10y^'+αy=0 ?
The solution for y^{''}-10y^'+αy=0 is y=c_{1}e^{(5+sqrt(-α+25))t}+c_{2}e^{(5-sqrt(-α+25))t}