Differential Equations
Differential Equations
star_batch_jee_advanced_2025
Grade 12
Question:
The general equation of the equation $y = px + \log p$ which does not contain the singular solution, is :
$y = cx + \log c$
$y = cx + \frac{1}{c}$
$y = \log x + c$
$y = -\log x + c$
Step-by-Step Solution
Key Concept: For Clairaut-type equations, the general solution is obtained by replacing the parameter with an arbitrary constant.
The general solution is obtained by replacing the parameter $p$ with an arbitrary constant $c$. Since $p = \frac{dy}{dx}$ appears in the original equation, the general solution is $y = cx + \log c$.
Correct Answer: 1