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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
2-56 Diff erential Equations
12.
3
(2)(35)0.xy ydx xdy ydx xdy+++=
Ans:
1
48 35
4
xy xy c+=
2.1.6 Linear Equations
A differential equation of the form
0120
() () ()( () 0)
dy
px pxy px px
dx
+= (2.73)
where
01
,pp
and
2
p
are continuous functions of x in some inter-
val I, is called a fi rst order linear differential equation in y. Dividing
Eq. (2.73) by
0
,p
we can write it as
() ()
dy
Pxy Qx
dx
+= (2.74)
which is taken as the standard form of the fi rst order linear equa-
tion. Here the dependent variable y and its derivative
dy
dx
occur
separately and to a fi rst degree. For example,
(i)
(1 ) 2 3
dy
xxyx
dx
2
++=
(ii)
cos (sin ) tan
dy
xxyx
dx
+=
If
() 0,Qx
/
then Eq. (2.73) ...
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Publisher Resources

ISBN: 9781299487406Publisher Website