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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
Formation of a Di erential Equation 1-9
Solution
–2xx
xy ae be x=+ + (1.27)
Differentiating (1.27) w.r.t. x
1
–2
xx
xy y ae be x+= +
(1.28)
Differentiating (1.28) w.r.t. x
21
22
xx
xy y ae be+=++ (1.29)
Eliminating a and b from (1.27) and (1.29)
2
21
2– –20xy y xy x++=
(1.30)
Example 1.2.8 Show that
22
1Ax By+= is a solution of
2
2
2
0
d y dy dy
xy y
dx dx dx
⎡⎤
⎛⎞
+−=
⎢⎥
⎜⎟
⎝⎠
⎢⎥
⎣⎦
Solution
22
1Ax By+= (1.31)
Differentiating (1.31) w.r.t. x
1
22 0Ax Byy+=
(1.32)
Differentiating (1.32) w.r.t. x
()
2
21
22 0AByyy++=
(1.33)
Eliminating A and B from (1.32) and (1.33)
()
2
21 1
–0xyy y yy+=
where
2
2
12
and
dy d y
yy
dx
dx
==
Example 1.2.9 Find the differential equation of ...
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Publisher Resources

ISBN: 9781299487406Publisher Website