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Previous year question hub

PDE Classification and Separation of Variables - Partial Differential Equations - Engineering Sciences Previous Year Questions

Practice PDE Classification and Separation of Variables - Partial Differential Equations - Engineering Sciences previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

7Papers
7Years
7Questions
1Topics

PDE Classification and Separation of Variables question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for PDE Classification and Separation of Variables. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 6 85.7%
Easy 1 14.3%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 6 85.7%
MSQ 1 14.3%

Subject weightage

Top subjects by unique question coverage.

Engineering Sciences
7 Qs

Most asked topics

Top topics across the included previous year papers.

Partial Differential Equations
7 Qs

Subtopic coverage

Top subtopics inside this exact selection.

PDE Classification and Separation of Variables
7 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Engineering Sciences (XE) 2026
1 Qs
Engineering Sciences (XE) 2025
1 Qs
Engineering Sciences (XE) 2022
1 Qs
Engineering Sciences (XE) 2019
1 Qs
Engineering Sciences (XE) 2016
1 Qs
Engineering Sciences (XE) 2013
1 Qs
Engineering Sciences (XE) 2007
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Engineering Sciences (XE) 202620261View paper
Engineering Sciences (XE) 202520251View paper
Engineering Sciences (XE) 202220221View paper
Engineering Sciences (XE) 201920191View paper
Engineering Sciences (XE) 201620161View paper
Engineering Sciences (XE) 201320131View paper
Engineering Sciences (XE) 200720071View paper

All PDE Classification and Separation of Variables previous year questions

Practice every matching question in batches of 20, with every available option.

1
2007 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2007
The general solution of \( x(z^2-y^2)\frac{\partial z}{\partial x} + y(x^2-z^2)\frac{\partial z}{\partial y} = z(y^2-x^2) \) is
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2
2013 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2013

Which one of the following partial differential equations CAN NOT be reduced to two ordinary differential equations by the method of separation of variables?

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3
2016 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2016
Which of the following is a quasi-linear partial differential equation?
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4
2019 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2019
If the transformation \(u(x, t) = e^x v(x, t)\) reduces the partial differential equation \(\frac{\partial^2 u}{\partial x^2} - 2\frac{\partial u}{\partial x} - \frac{\partial u}{\partial t} + u = 0\) to the equation \(\frac{\partial v}{\partial t} - \frac{\partial^2 v}{\partial x^2} = 9 f(x)\), then \(f(x)\) equals
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5
2022 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2022
If the partial differential equation \[ (x + 2) \frac{\partial^2 u}{\partial x^2} + 2(x + y) \frac{\partial^2 u}{\partial x \partial y} + 2(y - 1) \frac{\partial^2 u}{\partial y^2} - 3y^2 \frac{\partial u}{\partial y} = 0 \] is parabolic on the circle \((x - a)^2 + (y - b)^2 = r^2\), then the values of \(a, b\) and \(r\) are given by
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6
2025 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2025
Consider the second order Partial Differential Equation (PDE)
\(4x^2 \frac{\partial^2 u}{\partial x^2} + 4(x + y) \frac{\partial^2 u}{\partial x \partial y} + (x^2 + y^2) \frac{\partial^2 u}{\partial y^2} - u = 0.\)
Then which one of the following statements is correct ?
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7
2026 · Engineering Sciences · Partial Differential Equations · PDE Classification and Separation of Variables
Engineering Sciences (XE) 2026
Consider the following partial differential equation (PDE)
\((y - 1)\frac{\partial^2 u}{\partial x^2} - (x - 3)^2 \frac{\partial^2 u}{\partial y^2} + y^2 \frac{\partial u}{\partial x} + x^2 \frac{\partial u}{\partial y} + (x - y)u = 0.\)
Then, which of the following statements is/are true?
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