B.Sc Method Chapter 10 (Differential Equations of Higher Order) Notes

Sami Aslam

Mathematical Methods (B.Sc.)

Chapter:10 (Differential Equations of Higher Order)

In this chapter, we will study the following topics:

linear differential equations
homogeneous linear differential equations
nonhomogeneous equations
associated homogeneous equations
linear combination
linear dependent
particular solutions
general solutions
complementary function
particular integral
characteristics (or auxiliary) equation
real and distinct roots
real and equal roots
complex roots
differential operations
linear transformation
the linear differential equation of order n
nonhomogeneous linear equations
working rules for finding partial integral
principle of superposition
exponential shift
series expansion of the polynomial
expressions involving operators
binomial expansion
the method of undetermined coefficient
the exponential function
the sinusoidal function
principle of superposition
the cuachy euler equations
reduction of order
the wronskian
variation of parameters
one variable absent (non-linear d.e)
exact linear equations
the first integral
necessary and sufficient conditions
two special types of d.e
linear system of d.e
linear system with constant coefficients
power series solutions of first order d.e
second order linear equations
transcendental functions
find the series solution of Airy’s equation
applications of d.e
escape velocity
the harmonic oscillator equation
mass-spring system
period of oscillations

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