What is the solution for y^'+x*y=x*y^2 ?

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

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y^'+xy=xy^2

y^{^{'}} + x \cdot y = x \cdot y^{2}

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

Solution steps

y^{'} (x) + x \cdot y = x \cdot y^{2}

Solve separable ODE:

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

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

\frac{d y}{d x} = 3 x^{2} (- 2 y + 3)

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

y (81 - x^{2})^{\frac{1}{2}} d y = (81 + y^{2})^{\frac{1}{2}} d x

\frac{d y}{d x} = \frac{x y}{ln ( y )}, y = e, x = 7

x y^{^{'}} - (7 x + 1) y = 0

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