Question

The solution of differential equation dy=(4+y2)dx is:

• A. (A) y=2tan⁡(x+C)
• B. (B) y=2tan⁡(2x+C)
• C. (C) 2y=tan⁡(2x+C)
• D. (D) 2y=2tan⁡(x+C)

Answer 1

Answer: (B)

(B) y=2tan⁡(2x+C)

Answer 2

Explanation:
Concept:∫1a2+x2dx=1atan−1⁡xaGiven: dy=(4+y2)dx⇒dy4+y2=dxIntegrating both sides, we get∫dy22+y2=∫dx⇒12tan−1⁡y2=x+c⇒tan−1⁡y2=2x+Cy=2tan⁡(2x+C)Hence, the correct option is (B).