We can also classify differential equations as linear and non-linear.
A differential equation is called linear if the sum of the powers of the
function and its derivatives in each term is at most equal to unity, and
otherwise, non-linear.
Example 1.1.3
1. The following differential equations are linear.
(i)
2
012
2
()()()()
dydy
axaxaxybx
dxdx
++=
(ii)
2
2
2
0
dy
my
dx
+=
2. The following differential equations are non-linear:
(i)
2
2
dy
xy
dx
⎛⎞
=
⎜⎟
⎝⎠
(ii) tan
dy
y
dx
=
1.2 DIFFERENTIAL EQUATIONS
Differential equations arise in many engineering and physical
problems. The approach of an engineer to the study of differential
equations ...
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