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1.Exact differential equations 
2.Differential equations of first order and higher degree
3.Singular solution 
4.Orthogonal solution 
5.Linear equations with constant coefficients 
6.Linear equations with variable coefficients 
7.Linear equations of second order 
8.Simultaneous differential equations 
DIFFERENTIAL EQUATIONS- II

Max. Marks: 30
Time: 3 Hours
Int. Assessment: 3 Marks

Note: 1. The syllabus has been split into two units: Unit I and Unit II. Four questions will be set
from each unit.
2. A student will be asked to attempt five questions, selecting at least two questions from each
Unit. Each question will carry 6 marks.
3. The teaching time shall be five periods (45 minutes each) per paper per week, including
tutorial.
4. If internal assessment is to be conducted in the form of written examinations, then there will
be only one written examination in a semester.

Unit I
Series solution of differential equations—Power series method, Bessel and Legendre equations.
Bessel functions of the first and second kind. Legendre function. Generating function. Recurrence
relation and orthogonality of Bessel and Legendre functions.
Partial Differential Equations: Origin of first order Partial Differential Equations, Linear Equation of
first order, integral surfaces passing through a given curve, surfaces orthogonal to a given system of surfaces.

Unit II 
Inverse Laplace transforms: linearity property, shifting properties, change of scale property.
Inverse Laplace transforms of derivatives and integrals, Convolution theorem.
Applications of Laplace Transforms - Solution of differential equations with constant coefficients,
Solution of differential equations with variable coefficients, solution of simultaneous differential equations.
Laplace Transformation—Linearity of the Laplace Transformation. Existence theorem for Laplace
transformations, Shifting Theorems, Laplace transforms of derivatives and integrals, Multiplication of
Division by . 

Differential Equations-1, authored by Sanjay Gupta and published by Krishna Brothers, serves as an essential book for BA/BSc 2nd Year students enrolled in their 3rd semester at Panjab University, Chandigarh. This comprehensive guide delves into the essential principles and applications of differential equations, making it an indispensable resource for students seeking to excel in this critical area of mathematics.

The book meticulously explores various types of differential equations, catering to the diverse academic needs of learners. Understanding these mathematical concepts is essential for students pursuing degrees in mathematics, physics, engineering, and various related disciplines. Differential Equations-1 not only aligns with the curriculum for BA/BSc 2nd Year, Semester 3 but also prepares students for advanced studies and real-world applications.

The first chapter focuses on exact differential equations, presenting a clear and thorough explanation of the theory and providing numerous examples to reinforce understanding. This section lays the groundwork for more complex topics, enabling students to grasp the foundational concepts that will be essential for their future learning.

In the subsequent chapters, readers will explore differential equations of first order and higher degree, delving into the intricacies of these equations and their solutions. The book discusses concepts like singular solutions and orthogonal solutions, enhancing students' comprehension of the varied types of problem-solving techniques involved.

Sanjay Gupta's approach to complex subjects is accessible and engaging. He meticulously details linear equations with constant coefficients and linear equations with variable coefficients, ensuring that students gain a robust understanding of the methodologies and applications relevant to these equations. The chapter on linear equations of second order builds on earlier concepts, making it easy for students to transition from one topic to another while reinforcing their learning through organized presentation.

Additionally, the examination of simultaneous differential equations prepares students for real-world applications, illustrating how systems of equations can be solved simultaneously. This is particularly beneficial for students aspiring to careers in fields that require analytical and mathematical proficiency.

1.Exact differential equations 
2.Differential equations of first order and higher degree
3.Singular solution 
4.Orthogonal solution 
5.Linear equations with constant coefficients 
6.Linear equations with variable coefficients 
7.Linear equations of second order 
8.Simultaneous differential equations 

Have Doubts Regarding This Product ? Ask Your Question

DIFFERENTIAL EQUATIONS- II

Max. Marks: 30
Time: 3 Hours
Int. Assessment: 3 Marks

Note: 1. The syllabus has been split into two units: Unit I and Unit II. Four questions will be set
from each unit.
2. A student will be asked to attempt five questions, selecting at least two questions from each
Unit. Each question will carry 6 marks.
3. The teaching time shall be five periods (45 minutes each) per paper per week, including
tutorial.
4. If internal assessment is to be conducted in the form of written examinations, then there will
be only one written examination in a semester.

Unit I
Series solution of differential equations—Power series method, Bessel and Legendre equations.
Bessel functions of the first and second kind. Legendre function. Generating function. Recurrence
relation and orthogonality of Bessel and Legendre functions.
Partial Differential Equations: Origin of first order Partial Differential Equations, Linear Equation of
first order, integral surfaces passing through a given curve, surfaces orthogonal to a given system of surfaces.

Unit II 
Inverse Laplace transforms: linearity property, shifting properties, change of scale property.
Inverse Laplace transforms of derivatives and integrals, Convolution theorem.
Applications of Laplace Transforms - Solution of differential equations with constant coefficients,
Solution of differential equations with variable coefficients, solution of simultaneous differential equations.
Laplace Transformation—Linearity of the Laplace Transformation. Existence theorem for Laplace
transformations, Shifting Theorems, Laplace transforms of derivatives and integrals, Multiplication of
Division by . 

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