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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
Diff erential Equations of First Order and First Degree 2-21
Using (1, )
λ
as multipliers, each ratio
()
()( )
dy x
alxbmycn
λ
λλλ
+
=
+++ ++
(2.44)
Now, we determine
λ
such that
al
blm
λ
λ
+
=
+
or
2
() 0mbla
λλ
+− −= (2.45)
which is a quadratic in l and has two real distinct roots l
1
, l
2
if
2
()4 0.bl amΔ= + > More specifi cally
2
12
,()()42(0).bl bl am m m
λλ
⎡⎤
=− ± +
⎣⎦
Also,
(1,2)
i
i
i
al
i
bm
λ
λ
λ
+
==
+
each ratio
12
1112 22
() ()
11
dy x dy x
bmyxkbmy xk
λλ
λλ λλ
++
==⋅
++++++
(2.46)
;1,2
i
i
i
cn
ki
bm
λ
λ
⎛⎞
+
==
⎜⎟
+
⎝⎠
Integrating and dropping logs, the general solution of equation
(2.34) in this case may be written as
21
11 2 2
()( )
bm bm
yxk Cyxk
λλ
λλ
++
++ = ++ (2.47)
Note 2.1.21 ...
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Publisher Resources

ISBN: 9781299487406Publisher Website