What is the solution for yy^'+xy^2=(e^{-x^2}) ?

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

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yy^'+xy^2=(e^{-x^2})

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

f (x) = \frac{1}{3} x^{3} + 5.5 x^{2} + 30 x + 22

x \to 0 + lim (\frac{x ^{x} - 1}{2 x})

t \to 0 lim (1 + t^{3})

\int \frac{1}{12} cot (3 x) d x

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