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Question

Differential Equations Question on Differential Equations

For some real number c with 0 < c < 1, let φ:(1-c, 1 + c) -> (0,∞) be a differentiable function such that φ(1) = 1 and y = φ(x) is a solution of the differential equation (x2 + y2)dx-4xy dy = 0. Then which one of the following is true?

A

(3(φ(x))2 + x2)2 = 4x

B

(3(φ(x))2 - x2)2 = 4x

C

(3(φ(x))2 + x2)2 = 4φ(x)

D

(3(φ(x))2 - x2)2 = 4φ(x)

Answer

(3(φ(x))2 - x2)2 = 4x

Explanation

Solution

The correct option is (B): (3(φ(x))2 - x2)2 = 4x