Differential Equations
Linear Differential Equations
JEE Main 2022
Grade 12
Question:
The integrating factor of the differential equation $(1 - x^2)\frac{dy}{dx} - xy = 1$ is:
(1) $1 - x^2$
(2) $\sqrt{1 - x^2}$
(3) $\frac{1}{\sqrt{1 - x^2}}$
(4) $(1 - x^2)^{3/2}$
Step-by-Step Solution
Key Concept: First divide throughout by $(1 - x^2)$ to write the equation in the standard linear form $\frac{dy}{dx} + P(x)y = Q(x)$, then compute $e^{\int P(x) \, dx}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)