Home / Topic / Differential Equations
Topic Differential Equations
Asked 5 times in ESE over 4 years (2022–2026), peaking in 2022.
Key insights
- Most tested in ESE — 5 of 5 PYQs
- Most asked in 2022
- Recurs across 3 years (2022–2026)
Across exams
ESE · 5How the concept evolved
Rising — more than half its appearances (5 of 5) are since 2016.
Related concepts
Ideas UPSC tests alongside this one — keep exploring.
Sample questions
You've seen the pattern — here are a few of the actual PYQs.
ESE2026
The solution of differential equation y' = (xy² − cos x sin x)/(y(1−x²)), y(0) = 2 is
- A y²(1 + x²) − cos²x = 3
- B y²(1 − x²) + cos²x = 5
- C y²(1 − x²) + cos²x = 7
- D y²(1 − x²) − cos²x = 3
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2026
The solution of differential equation y'' + 4y' + 3y = e^t ; y(0) = 0, y'(0) = 2 is
- A y(t) = (e^t − 7e^{-3t})/8 + (3e^{-t})/4
- B y(t) = (e^t − 5e^{-3t})/8 + (3e^{-t})/4
- C y(t) = (e^t + 7e^{-3t})/8 − (3e^{-t})/4
- D y(t) = (e^t + 7e^{-3t})/8 + (3e^{-t})/4
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2025
Consider the following equation: (x + y + 1) dx + (2x + 2y + 3) dy = 0 Solving the equation will be
- A u – log(u + 1) = x + c
- B 2u + log(u – 1) = x + c
- C 2u – log(u + 1) = x + c
- D u + log(u – 1) = x + c
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
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