B.Sc Method Chapter 9 (First Order Differential Equations) Notes

Sami Aslam

Mathematical Methods (B.Sc.)

Chapter:09 (First Order Differential Equations)

In this chapter, we will study the following topics:

d.e. and their classifications
ordinary differential equations
dependent variables
order of a differential equation
partial differential equation
the degree of a differential equation
a solution or integral of a differential equation
nonlinear differential equation
formation of differential equations
initial and boundary condtions
one-point boundary conditions
initial value problems
two-point boudary conditions
arbitrary constant
separable equations or separable variables
homogeneous equations
D.E. reducible to the homogeneous form
exact differential
solution of exact differential equations
inetegrating factors
linear equations
the bernoulli equations
orthogonal trajectories
polar coordinates
equations solvable for P
equations solvable for y
equations solvable for x
clairaut’s equation
envelope
neighboring curves
the equation of the envelope
c-discriminant
singular solutions
p-discriminant
the ricatti equation

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