The differential equation x dy dx =2y represents _____

MHT CET 2025 Mathematics question

The differential equation represents

(A)a family of circles with radius c
(B)a family of parabolas with vertex at the origin and axis along the positive Y-axisCorrect
(C)a family of parabolas with vertex the at origin and axis along the positive X-axis
(D)a family of ellipses

Answer: (B)

Separate variables: . Integrate: . This is a parabola with vertex at the origin, symmetric about the y-axis (the equation has the form ), so the

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Question ID VK-102902