Which one of the following is the differential equation that represents the family of curves $y = \frac{1}{{2{x^2} - c}}$ where c is an arbitrary constant?

Question

Which one of the following is the differential equation that represents the family of curves $y = \frac{1}{{2{x^2} - c}}$ where c is an arbitrary constant?

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

$\frac{{dy}}{{dx}} = 4x{y^2}$

TuteeHUB · Answer

$\frac{{dy}}{{dx}} = \frac{1}{y}$

TuteeHUB · Answer

$\frac{{dy}}{{dx}} = {x^2}y$

TuteeHUB · Answer

$\frac{{dy}}{{dx}} = - 4x{y^2}$

1.	Which one of the following is the differential equation that represents the family of curves \(y = \frac{1}{{2{x^2} - c}}\) where c is an arbitrary constant?
A.	\(\frac{{dy}}{{dx}} = 4x{y^2}\)
B.	\(\frac{{dy}}{{dx}} = \frac{1}{y}\)
C.	\(\frac{{dy}}{{dx}} = {x^2}y\)
D.	\(\frac{{dy}}{{dx}} = - 4x{y^2}\)
Answer» E.

Which one of the following is the differential equation that represents the family of curves \(y = \frac{1}{{2{x^2} - c}}\) where c is an arbitrary constant?

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