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+9))+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 + 9)) + 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 + 9)) + c_{1}}

y = e^{- 12 (\frac{1}{8} l n (x + 1) - \frac{1}{8} l n (x + 9)) + c_{1}}

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (16)

\frac{d y}{d x} = \frac{- 0.1}{cos ( y )}, y (0) = \frac{π}{3}

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

y^{^{'}} - 12 x y = 9 x

e^{x} y d y - (e^{- y} + 2 e^{2 x - y}) d x = 0

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+9))+c_{1}}