Question:
The general solution of $\frac{ydx - xdy}{y^2} = 0$ represents a family of}
The general solution of $\frac{ydx - xdy}{y^2} = 0$ represents a family of}
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$ydx-xdy$ involves the quotient rule. $xdy+ydx$ involves the product rule ($d(xy)$).
Updated On: Jul 4, 2026
- Straight lines passing through the origin
- Circles
- parabolas
- Hyperbolas
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Recognize the expression as the derivative of a quotient: $d(\frac{x}{y}) = \frac{ydx - xdy}{y^2}$.
Step 2: Meaning
The equation is $d(\frac{x}{y}) = 0$.
Step 3: Analysis
Integrating both sides gives $\frac{x}{y} = c$, where $c$ is a constant.
Step 4: Conclusion
$x = cy$ or $y = mx$ (where $m=1/c$) is the equation of a straight line passing through the origin. Final Answer: (A)
Recognize the expression as the derivative of a quotient: $d(\frac{x}{y}) = \frac{ydx - xdy}{y^2}$.
Step 2: Meaning
The equation is $d(\frac{x}{y}) = 0$.
Step 3: Analysis
Integrating both sides gives $\frac{x}{y} = c$, where $c$ is a constant.
Step 4: Conclusion
$x = cy$ or $y = mx$ (where $m=1/c$) is the equation of a straight line passing through the origin. Final Answer: (A)
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