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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
2-44 Diff erential Equations
(iv)
22
2
0
1
ydx xdy dx
xy
x
+=
+
()
()
()
2
2
2
2
2
11
0
1
1
0
1
1
sin tan .
ydx xdy
x
y
x
y
x
y
x
dx
x
d
dx
x
y
xc
x
−−
⇒+=
+
⇒+=
+
⇒=+
(v)
22
22
tan 0
xdx ydy
xdx
xy
+
+=
+
22
22
(log( )) (log(sec )) 0
( )(sec ) .
dxyd x
xy xc
⇒++ =
⇒+ =
(vi) ()0ydx xdy xy ydx xdy++ =
2
()
0
()
1
log .
dxy dx dy
xy x y
x
c
xy y
⇒+−=
⇒− + =
EXERCISE 2.5
Find the integ
rating factors by inspection and solve the following:
1.
2
(3) 0.xdy y x dx−− =
Ans:
3
y
xc
x
+=
2.
2
2.
xx
ye e dy xy dx
−−
+=
Ans:
2
x
e
y
xc
=+
3.
2
22.xdy ydx y xdy+=
Ans:
2
2 y
xy ce=
4.
22 22
()( )()( )
.
xyxdyydx xyxdxydy+−=−+
Ans:
22
()()( )xy cxyx y+= +
Ch02.indd 44Ch02.indd 44 12/9/2011 11:37:01 AM12/9/2011 11:37:01 AM
Diff
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Publisher Resources

ISBN: 9781299487406Publisher Website