An answer I get with the Bernoulli Method doesn't check

[Jeff12341234]

When I plug what I get for y back into the original Eq. to check it, it doesn't pass. I did something wrong somewhere but it all seems right to me. Where did I go wrong?

 

[Mute]

You made a mistake in going from the first line to the second: you divided by $3(1+x^2)$ but did not distribute the division to the $2xy^4$ term. Your second line should look like

$$\frac{dy}{dx} +\frac{2xy}{3(1+x^2)} = \frac{2xy^4}{3(1+x^2)}.$$

Try your calculation again and see if it works out.