RGPV Maths 2 Unit 3 Notes PDF | Partial Differential Equations

Unit 3: Partial Differential Equations Overview

Maths 2 Unit 3 covers Partial Differential Equations. This unit is important for RGPV exams because questions are repeatedly asked from formation of PDE, Lagrange’s linear PDE, Charpit’s method, homogeneous linear PDE with constant coefficients and operator method.

According to the uploaded notes, Unit 3 includes formulation of PDE, linear PDE, non-linear PDE and homogeneous linear PDE with constant coefficients. :contentReference[oaicite:0]{index=0}

Exam Focus: Lagrange’s PDE, Homogeneous PDE, Operator Method, Formation of PDE and Charpit’s Method are high-priority topics.

Unit 3 Syllabus

Formulation of Partial Differential Equations
Formation of PDE by Eliminating Arbitrary Constants
Formation of PDE by Eliminating Arbitrary Functions
Linear Partial Differential Equations
Non-Linear Partial Differential Equations
Lagrange’s Linear PDE
Charpit’s Method
Homogeneous Linear PDE with Constant Coefficients
Differential Operators D and D'
Auxiliary Equation Method
Complementary Function and Particular Integral
Operator Method for PDE
Reducible PDE Equations
PDE with Exponential and Trigonometric Functions

Most Important Topics for Exam

Lagrange’s PDE

Most repeated first order linear PDE topic using auxiliary equations.

Homogeneous PDE

Very important for constant coefficient problems and CF.

Operator Method

High-priority numerical method for solving PDE.

Formation of PDE

Frequently asked by eliminating arbitrary constants or functions.

Charpit’s Method

Important for solving non-linear first order PDE.

CF and PI

Commonly asked in homogeneous linear PDE with constant coefficients.

Short Notes for Quick Revision

1. Partial Differential Equation

A differential equation involving partial derivatives of a dependent variable with respect to two or more independent variables is called Partial Differential Equation.

2. Order of PDE

The order of a PDE is the order of the highest partial derivative present in the equation.

3. Degree of PDE

The degree of PDE is the power of the highest order partial derivative after removing radicals and fractions.

4. Formation of PDE

PDE is formed by eliminating arbitrary constants or arbitrary functions from the given relation.

5. Linear PDE

A PDE is linear if dependent variable and its partial derivatives occur linearly.

6. Non-Linear PDE

A PDE is non-linear if derivatives occur with powers, products or non-linear functions.

7. Lagrange’s Linear PDE

Standard form of Lagrange’s PDE is Pp + Qq = R, where p = ∂z/∂x and q = ∂z/∂y.

8. Lagrange Auxiliary Equations

For Pp + Qq = R, auxiliary equations are dx/P = dy/Q = dz/R.

9. Charpit’s Method

Charpit’s method is used to solve non-linear partial differential equations of first order.

10. Homogeneous Linear PDE with Constant Coefficients

A PDE of the form F(D,D')z = 0 is called homogeneous linear PDE with constant coefficients.

11. Operators D and D'

D = ∂/∂x and D' = ∂/∂y are differential operators used in PDE operator method.

12. Complementary Function

Complementary Function is obtained by solving auxiliary equation of PDE.

13. Particular Integral

Particular Integral depends on the right-hand side function of PDE.

14. Complete Solution

The complete solution of linear PDE is z = C.F. + P.I.

Important Formula Sheet

Topic	Formula / Standard Form
Standard Linear PDE	Pp + Qq = R
Lagrange Auxiliary Equations	dx/P = dy/Q = dz/R
Differential Operator	D = ∂/∂x
Differential Operator	D' = ∂/∂y
Homogeneous Linear PDE	F(D,D')z = 0
General Solution	z = C.F. + P.I.
Particular Integral	P.I. = 1/F(D,D') × RHS
Exponential Rule	P.I. = e^ax+by / F(a,b)

PDE Methods Table

Method	Used For
Eliminating Arbitrary Constants	Formation of PDE from equations containing constants
Eliminating Arbitrary Functions	Formation of PDE from equations containing arbitrary function
Lagrange’s Method	First order linear PDE
Charpit’s Method	First order non-linear PDE
Operator Method	Linear PDE with constant coefficients
Auxiliary Equation Method	Finding complementary function

Most Important Questions

Form partial differential equations by eliminating arbitrary constants.
Form partial differential equations by eliminating arbitrary functions.
Solve first order linear PDE using Lagrange’s method.
Solve non-linear PDE using Charpit’s method.
Solve homogeneous linear PDE with constant coefficients.
Solve PDE using operator method.
Solve: (D² − DD' − 2D'²)z = 0.
Solve: (D² − 3DD' + 2D'²)z = e^x+y.
Solve: (D − D')²z = sin(x+y).
Solve: (D² + DD' − 2D'²)z = cos(x−y).
Find complementary function and particular integral of PDE.
Solve reducible PDE equations.

These questions are based on the uploaded Unit 3 Important Questions PDF. :contentReference[oaicite:1]{index=1}

PYQ Analysis Table

According to the uploaded Unit 3 PYQ analysis, formation of PDE, Lagrange’s linear PDE, homogeneous PDE with constant coefficients, operator method and Charpit’s method are repeatedly asked from 2022–2025 papers. :contentReference[oaicite:2]{index=2}

Topic	Repeated Pattern	Frequency
Lagrange’s PDE	First order linear PDE using auxiliary equations	⭐⭐⭐⭐⭐
Homogeneous PDE	Constant coefficient PDE and auxiliary equation	⭐⭐⭐⭐⭐
Operator Method	Find C.F. and P.I. using D and D'	⭐⭐⭐⭐⭐
Formation of PDE	Eliminating arbitrary constants/functions	⭐⭐⭐⭐
Charpit’s Method	Non-linear first order PDE	⭐⭐⭐⭐
Reducible PDE	Reducible equations to standard form	⭐⭐⭐

High Chance Questions for Next Exam

Form PDE by eliminating arbitrary constants/functions.
Solve first order PDE using Lagrange’s method.
Solve PDE using Charpit’s method.
Solve homogeneous PDE with constant coefficients.
Solve PDE using operator method.
Solve equations involving exponential and trigonometric functions.
Solve reducible PDE equations.

Very Important Numerical Practice

Question Type	Practice Problem
Homogeneous PDE	Solve: (D² − DD' − 2D'²)z = 0
Exponential RHS	Solve: (D² − 3DD' + 2D'²)z = e^x+y
Trigonometric RHS	Solve: (D − D')²z = sin(x+y)
Trigonometric RHS	Solve: (D² + DD' − 2D'²)z = cos(x−y)
Lagrange Method	Solve first order PDE using dx/P = dy/Q = dz/R
Formation of PDE	Form PDE by eliminating arbitrary constants/functions

Topic Weightage Analysis

Topic	Importance
Lagrange’s PDE	⭐⭐⭐⭐⭐
Homogeneous PDE	⭐⭐⭐⭐⭐
Operator Method	⭐⭐⭐⭐⭐
Formation of PDE	⭐⭐⭐⭐
Charpit’s Method	⭐⭐⭐⭐
Reducible PDE	⭐⭐⭐

Download Maths 2 Unit 3 PDFs

Download complete Unit 3 notes, important questions and PYQ analysis for RGPV Engineering Mathematics-II exam preparation.

PYQ Analysis

How to Prepare Maths 2 Unit 3

First understand the meaning of PDE, order and degree.
Practice formation of PDE by eliminating constants and functions.
Learn Lagrange auxiliary equations properly.
Practice operator method problems daily.
Revise C.F. and P.I. rules for PDE.
Practice exponential and trigonometric RHS questions.
Prepare Charpit’s method for non-linear PDE.

Frequently Asked Questions

Is Maths 2 Unit 3 important for RGPV exams?

Yes, Unit 3 is very important because Lagrange’s PDE, operator method and homogeneous PDE are repeatedly asked.

Which topic is most important in Maths 2 Unit 3?

Lagrange’s PDE, Homogeneous PDE with Constant Coefficients and Operator Method are the most important topics.

Are numericals asked from Unit 3?

Yes, Unit 3 is mainly numerical-based. Questions are asked from formation of PDE, Lagrange method, Charpit method and operator method.

How should I prepare Unit 3 quickly?

Focus on Lagrange’s method, formation of PDE, operator method, C.F., P.I. and repeated PYQ numericals.

Is this website official?

No, this is an independent educational website created only for student support and exam preparation.

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