Question:
The solution of $p = \tan(px - y)$ is (where $p = \frac{dy}{dx}$)
The solution of $p = \tan(px - y)$ is (where $p = \frac{dy}{dx}$)
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Clairaut's form $y = px + f(p)$ always has the general solution $y = cx + f(c)$. Just swap $p$ for $c$!
Updated On: Jul 3, 2026
- $y = \tan^{-1}x + c$
- $y = \frac{c}{x} + \tan^{-1}c$
- $y = cx - \tan^{-1}c$
- $xy = \tan^{-1}c$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
This is a differential equation solvable for $y$, specifically in the form of Clairaut's Equation $y = px + f(p)$.
Step 2: Meaning
Rearranging the given equation: $\tan^{-1}p = px - y$, which becomes $y = px - \tan^{-1}p$.
Step 3: Analysis
In Clairaut's form $y = px + f(p)$, the general solution is obtained by simply replacing $p$ with a constant $c$.
Step 4: Conclusion
Substituting $p = c$ into $y = px - \tan^{-1}p$, we get the general solution: $y = cx - \tan^{-1}c$. Final Answer: (C)
This is a differential equation solvable for $y$, specifically in the form of Clairaut's Equation $y = px + f(p)$.
Step 2: Meaning
Rearranging the given equation: $\tan^{-1}p = px - y$, which becomes $y = px - \tan^{-1}p$.
Step 3: Analysis
In Clairaut's form $y = px + f(p)$, the general solution is obtained by simply replacing $p$ with a constant $c$.
Step 4: Conclusion
Substituting $p = c$ into $y = px - \tan^{-1}p$, we get the general solution: $y = cx - \tan^{-1}c$. Final Answer: (C)
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