What is the solution for y^{''}+(3-α)y^'-2(α-1)y=0 ?

The solution for y^{''}+(3-α)y^'-2(α-1)y=0 is y=c_{1}e^{(α-1)t}+c_{2}e^{-2t}

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y^{''}+(3-α)y^'-2(α-1)y=0

y^{^{''}} + (3 - α) y^{^{'}} - 2 (α - 1) y = 0

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

Solution steps

y^{''} (t) + (3 - α) y^{'} (t) - 2 (α - 1) y = 0

Solve linear ODE:

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

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

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{''}} (0) = 13

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 5 y = 0

x^{^{''}} + c x = 0

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

What is the solution for y^{''}+(3-α)y^'-2(α-1)y=0 ?
The solution for y^{''}+(3-α)y^'-2(α-1)y=0 is y=c_{1}e^{(α-1)t}+c_{2}e^{-2t}