Q. The equation of the curve through the point (3, 2) and whose slope is $\frac{x^{2}}{y + 1}$, is
A) $\frac{y^{2}}{2} + y = \frac{x^{3}}{3} + 5$
B) $y + y^{2} - x^{3} - 21$
C) $y^{2} + 2y = \frac{2x^{3}}{3} - 10$
D) $\frac{y^{2}}{2} + y = \frac{x^{3}}{3} - 5$
Explanation
(d)
Given that, $\frac{dy}{dx} = \frac{x^{2}}{y + 1}$
$\Rightarrow (y + 1)dy = x^{2}dx$
$\Rightarrow \frac{y^{2}}{2} + y = \frac{x^{2}}{3} + c$
This curve passes through the point (3, 2).
$2 + 2 = 9 + c$
$\Rightarrow c = - 5$
$\therefore$ Required curve is $\frac{y^{2}}{2} + y = \frac{x^{3}}{3} - 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.