Question

Solve the equation (Tricky Equation!)
Separable!
(x+xy^2)dx+e^x^2 ydy=0

Answer 1

\[(x+xy ^{2})dx+e ^{x ^{2}}ydy=0\]

Answer 2

x(1 + y^2) dx = - (e^x^2) y dy
-x e^(-x^2) dx = y/(1+y^2) dy integrating
-1/2 e^(-x^2) = 1/2 ln(1 + y^2) + C

-e^(-x^2) = ln(1 + y^2) + C
ln(1 + y^2) = C - e^(-x^2) because the constant is still arbitrary

y^2 + 1 = e^[C - e^(-x^2)]
and thus you can generate two possible functions of y in terms of x soon.

Answer 3

okay THANKS! give me 100000 seconds to process that please

Answer 4

You're welcome!! Xo!