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

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

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

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

y = \frac{e ^{\frac{- x ^{2} + 2 x + c _{1}}{2}}}{x ^{2}}

Solution steps

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

Solve separable ODE:

y = \frac{e ^{\frac{- x ^{2} + 2 x + c _{1}}{2}}}{x ^{2}}

y = \frac{e ^{\frac{- x ^{2} + 2 x + c _{1}}{2}}}{x ^{2}}

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