Question

The solution of the differential equation \(\displaystyle \frac{dy}{dx}=1+y^2\) is

• A. \(y=\tan x+c\)
• B. \(y=\tan(x+c)\)
• C. \(y=\tan x\)
• D. \(y=-\tan(x+c)\)

Hint:

For \(\frac{dy}{dx}=1+y^2\), separate variables and use \(\int\frac{dy}{1+y^2}=\tan^{-1}y\).

Answer 1

The Correct Option is B