What is the solution for (x-1)^2y^'+8(x-1)y^'+12y=0 ?

The solution for (x-1)^2y^'+8(x-1)y^'+12y=0 is y=e^{-12(1/8 ln(x-1)-1/8 ln(x+7))+c_{1}}

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(x-1)^2y^'+8(x-1)y^'+12y=0

(x - 1)^{2} y^{^{'}} + 8 (x - 1) y^{^{'}} + 12 y = 0

y = e^{- 12 (\frac{1}{8} l n (x - 1) - \frac{1}{8} l n (x + 7)) + c_{1}}

Solution steps

(x - 1)^{2} y^{'} (x) + 8 (x - 1) y^{'} (x) + 12 y = 0

Solve separable ODE:

y = e^{- 12 (\frac{1}{8} l n (x - 1) - \frac{1}{8} l n (x + 7)) + c_{1}}

y = e^{- 12 (\frac{1}{8} l n (x - 1) - \frac{1}{8} l n (x + 7)) + c_{1}}

\frac{d y}{d x} = \frac{4 x}{y ^{2}}

y^{^{'}} = \frac{2 y ^{4} + 2}{4 x y ^{3}}

y^{^{'}} = y + 5, y (0) = 11 e^{x} - 5

\frac{d y}{d x} = e^{(6 y + 7 x)}, y (0) = 15

50 y^{^{'}} + 20 y^{^{'}} + y = 5000

What is the solution for (x-1)^2y^'+8(x-1)y^'+12y=0 ?
The solution for (x-1)^2y^'+8(x-1)y^'+12y=0 is y=e^{-12(1/8 ln(x-1)-1/8 ln(x+7))+c_{1}}