Which of the following implicit relations represents a family of solutions to the…

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

Problem

Which of the following implicit relations represents a family of solutions to the differential equation

y\,\dfrac{dy}{dx}=x

? (In each option

C

is an arbitrary constant.) (a)

y^{2}=2x+C

(b)

y^{2}=x^{2}+C

(c)

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

(d)

y^{2}=2x^{2}+C