Differential Equations
Variable Separable Form
JEE Main 2018
Grade 12
Question:
The general solution of $\frac{dy}{dx} = \frac{1 + y^2}{1 + x^2}$ is:
(1) $\tan^{-1} y + \tan^{-1} x = C$
(2) $\tan^{-1} y - \tan^{-1} x = C$
(3) $\tan(y - x) = C$
(4) $y - x = C(1 + xy)$
Step-by-Step Solution
Key Concept: Separate the variables by writing the equation as $\frac{dy}{1 + y^2} = \frac{dx}{1 + x^2}$, and integrate both sides directly.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)