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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
Linear Equation of the Second Order with Variable Coeffi cients 5-3
Integrating we get
12
22
Pdx Pdx
Pdx
ee
V Ru e dx dx c dx c
uu
−−
⎡⎤
∫∫
⎢⎥
=++
⎢⎥
⎣⎦
∫∫
Substituting this value of v in (5.2) we get
21
22
Pdx Pdx
Pdx
ee
ycucu dxu Rue dx
uu
−−
⎡⎤
∫∫
⎢⎥
=+ +
⎢⎥
⎣⎦
∫∫∫
Since this includes the known solution ()yux= and it contains two
arbitrary constants, it is the general solution of (5.1).
5.1 TO FIND THE INTEGRAL IN C.F. BY INSPECTION,
i.e. TO FIND A SOLUTION OF
2
2
0
dy dy
pQy
dx dx
++=
+ + =
2
2
0
dy dy
PQy
dx dx
++=
(5.8)
1.
mx
ye=
is a solution of (5.8) if
2
0mpmQ++=
we have
2
2
2
,
mx mx mx
dy d y
ye me me
dx dx
== =
If
mx
ye=
is a solution of (5.8) then
()
2
() 0
mx
mPmQe++ =
2
0mPmQ++
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Publisher Resources

ISBN: 9781299487406Publisher Website