17/09/2026
Can you form the required Partial Differential Equation by eliminating \(a,b,c\)? 🤔
Given:
$$ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 $$
The challenge is to eliminate the arbitrary constants \(a,b,c\) and obtain the required PDE.
This problem involves:
✅ Partial Differentiation
✅ Formation of Partial Differential Equations
✅ Elimination of Arbitrary Constants
✅ First & Second Partial Derivatives
✅ Higher-Order Partial Differential Equations
✅ Application of PDE concepts
✅ UPSC Mathematics Optional – Paper I
📌 A strong command of differentiation and systematic elimination is essential when solving these problems.
🧠 CHALLENGE FOR ASPIRANTS:
Before checking the solution in the image, try deriving the PDE yourself.
Can You Eliminate Arbitrary Functions in This UPSC Maths PDE? 🤯
UPSC Maths Optional aspirants — can you solve this Partial Differential Equation problem?
In this question, we eliminate the arbitrary functions from:
z = f(x² − y) + g(x² + y)
The solution demonstrates how to differentiate partially, combine the resulting equations, and obtain the required second-order PDE.
This is an important type of problem for UPSC IAS/IFoS Mathematics Optional, especially for strengthening your understanding of Partial Differential Equations (PDEs) and exam-oriented answer writing.
🎯 Prepare smarter with IMS4Maths by K. Venkanna Sir — with a focus on syllabus coverage, answer writing, practice, tests and personalised guidance.
👉 Explore UPSC Maths Optional courses and preparation resources:
IMS4Maths – Mathematics Optional for UPSC IAS/IFoS
Comment your answer before checking the solution!
