What is the solution for f(x)x+xf^'(x)x+x^2f(x)x=0 ?

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

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f(x)x+xf^'(x)x+x^2f(x)x=0

f (x) x + x f^{^{'}} (x) x + x^{2} f (x) x = 0

f (x) = \frac{e ^{\frac{- x ^{2} + c _{1}}{2}}}{x}

Solution steps

f (x) x + x f^{'} (x) x + x^{2} f (x) x = 0

Solve separable ODE:

f (x) = \frac{e ^{\frac{- x ^{2} + c _{1}}{2}}}{x}

f (x) = \frac{e ^{\frac{- x ^{2} + c _{1}}{2}}}{x}

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