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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 2-9
18.
2
31
dy dy
y
xx
dx dx
⎛⎞
−=+
⎜⎟
⎝⎠
.
Ans:
(
)
(
)
–3 3 1yxcx+=
19.
()
1cos sin 0
yy
e x dx e x dy++ =.
Ans:
()
1sin
y
exc+=
20.
1
2
cos 2 0
y
yxxedy=
.
Ans:
1
sin + =
y
xe c
21.
()
2
3 cos 1 cot 0
xx
e y dx e y dy++ =
.
Ans:
()
3
tan 1
x
yc e=+
22.
(
)
cos x y dy dx+=.
Ans:
tan
2
xy
yc
+
⎛⎞
=+
⎜⎟
⎝⎠
23.
1
xy
dy
e
dx
+
+= .
Ans:
(
)
10
xy
xce
+
++=
24.
xyady xya
xybdx xyb
⎛⎞⎛⎞
+− ++
=
⎜⎟⎜⎟
+− ++
⎝⎠⎝⎠
.
Ans:
(
)
(
)
(
)
2
1
log 2
2
xy ba xy ab xc
⎡⎤
++ + = +
⎣⎦
2.1.2 Homogeneous Equations
A polynomial f (x, y) is called a homogeneous function of degree n if
(,) (,)
n
ftxty tfxy=
for some tR or equivalently,
(,) (1, ).
n
fxy xf yx=
Example 2.1.10 (, ) 2 3fxy
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Publisher Resources

ISBN: 9781299487406Publisher Website