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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
2-68 Diff erential Equations
19.
log 2log .
dy
xx y x
dx
+=
Ans:
(
)
2
log log yxc x=+
20.
sin cos sin .
dy
xx y x
dx
=+
Ans:
cot log tan
2
x
yxc=+
21.
(
)
1
tan 1 sec .
1
x
dy
yxey
dx x
−=+
+
Ans:
(
)
()
sin 1
x
yxec=+ +
22.
2
1–2
1.
dy x
y
dx x
+=
Ans:
()
2
21
y
xe x=+
23.
()
22
1
.
121
dy x
y
dx x x x
+=
++
Ans:
2–1
11
1logtantan
22
yxc x
⎛⎞
+=+
⎜⎟
⎝⎠
24.
()()
22
10.yxydx xxdy++ + + =
Ans:
–1
–tanxy c x=
2.1.7 Bernoulli’s Equation
An equation of the form
(,1)
a
dy
Py Qy a R a
dx
+= (2.91)
is called Bernoulli’s equation.
Bernoulli’s equation is reducible to the linear for
m by the substitu-
tion
1
.
a
zy
=
Multiplying Eq. (2.91) by
(1 ) ,
a
ay
it becomes
1
(1 ) (1 ) (1 )
aa
dy
ay P ay Q a
dx
−−
−+−=−
(2.92)
Ch02.indd 68
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Publisher Resources

ISBN: 9781299487406Publisher Website