Differential Equations
Homogeneous Differential Equations
JEE Main 2020
Grade 12
Question:
The general solution of $\frac{dy}{dx} = \frac{x + y}{x}$ is:
(1) $y = x \ln |x| + C$
(2) $y = x(\ln |x| + C)$
(3) $y = \ln |x| + Cx$
(4) $y = Cx \ln |x|$
Step-by-Step Solution
Key Concept: Rewrite the right side as $1 + \frac{y}{x}$ and substitute $y = vx$ to make the equation variables-separable in $v$ and $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)