Differential Equations
Differential Equations
Allen Star Batch
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's form equations y = px + f(p), the general solution is obtained by replacing the parameter p with an arbitrary constant c. The singular solution is the envelope of the family of lines, found by eliminating p from y = px + f(p) and dy/dp = 0.
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

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