What is the solution for y^{''}-(2α-1)y^'+α(α-1)y=0 ?

The solution for y^{''}-(2α-1)y^'+α(α-1)y=0 is y=c_{1}e^{αt}+c_{2}e^{(α-1)t}

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y^{''}-(2α-1)y^'+α(α-1)y=0

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

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

Solution steps

y^{''} (t) - (2 α - 1) y^{'} (t) + α (α - 1) y = 0

Solve linear ODE:

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

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

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