Question
If y x is the solution of the differential equation x d y - y 2 - 4 y d x = 0 for x > 0 ,   y 1 = 2 , and the slope of the curve y = y x is never zero, then the value of 10 y 2 is _____ .
JEE Advanced
Mathematics
Differential Equations
2022
JEE Advanced 2022 (Paper 2)
JEE Advanced Mathematics Question (2022) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
Given differential equation is d y y 2 - 4 y = d x x ⇒ 1 4 1 y - 4 - 1 y d y = d x x Integrating both sides, we get, 1 4 ln y - 4 y = ln x + c Given, y 1 = 2 i.e. c = 0 So, y - 4 y = ± x 4 or, y = 4 1 ± x 4 Considering y = 4 1 + x 4 So, 10 y 2 = 10 4 1 + 4 = 8
Related: Mathematics — Differential Equations · All PYQ Banks