Let . Which of the following is a correct implicit form of the general…

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

Let

\displaystyle \frac{dy}{dx}=\frac{2x}{1+y^{2}}

. Which of the following is a correct implicit form of the general solution? (a)

\arctan y=x^{2}+C

(b)

\dfrac{y^{2}}{2}+\dfrac{y^{4}}{4}=x^{2}+C

(c)

y+\dfrac{y^{3}}{3}=x^{2}+C

(d)

y+\dfrac{y^{3}}{3}=2x+C