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