Question

The solution of differential equation $dy=(4+y^2)dx$ is:

• (A) $y=2\tan (x+C)$
• (B) $y=2\tan (2x+C)$
• (C) $2y=\tan (2x+C)$
• (D) $2y=2\tan (x+C)$

Answer 1

The Correct Option is B

Explanation:
Concept:$\int \frac{1}{a^2+x^2}dx=\frac{1}{a}{\tan }^{-1}\frac{x}{a}$Given: $dy=(4+y^2)dx$$\Rightarrow \frac{dy}{4+y^2}=dx$Integrating both sides, we get$\int \frac{dy}{2^2+y^2}=\int dx$$\Rightarrow \frac{1}{2}{\tan }^{-1}\frac{y}{2}=x+c$$\Rightarrow {\tan }^{-1}\frac{y}{2}=2x+C$$y=2\tan (2x+C)$Hence, the correct option is (B).