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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
4-16 Diff erential Equations
()()
33
12 212 0
dp
ppxxpx
dx
+++ =
()
3
12 2 0
dp
px p x
dx
⎛⎞
++=
⎜⎟
⎝⎠
20
dp
px
dx
+=
Separating the variables and integrating
22
20loglog+= = ⇒=
dp dx c
px c p
px x
Eliminating p from this and the given relation. We get
()
2
24 22
–4yxp xp=
()
2
22 2 2
–4
⎛⎞
=
⎜⎟
⎝⎠
c
yxc x x
x
()
2
2
–4yc cx=
The general solution is
()
2
2
–4yc cx=
Example 4.2.9 Solve y + px = p
2
x
4
.
Solution y + px = p
2
x
4
y = px + p
2
x
4
Differentiating w.r.t. x and denoting
dy
dx
by p we get
423
–2 4
dp dp
ppx px xp
dx dx
=− + +
()
23 3
2– 1–2 0
dp
ppxx xp
dx
+=
()()
33
21–2 1–2 0
dp
pxpx xp
dx
+=
Ch04.indd 16Ch04.indd 16 12/9/2011 11:49:03 AM12/9/2011 11:49:03 AM
Diff erential Equations of the First Order but not ...
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Publisher Resources

ISBN: 9781299487406Publisher Website