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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 Diff erential Equations with Constant Coeffi cients 3-63
13.
()
3
1sin32.
x
Dye x−=+ +
[JNTU 2004(1)]
Ans:
⎛⎞
⎛⎞ ⎛⎞
=+ +
⎜⎟
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
⎝⎠
++
2
12 3
33
cos sin
22
1
(27cos3 sin3 ) 2
3 730
xx
x
yce e c x c x
x
exx
14.
()
2
1cos2 0Dxttxx+= ==
at
0.t =
[JNTU 2002]
Ans:
54
( ) sin cos2 sin 2
93 9
t
xt t t t=− +
15.
()
222
44 8 sin2.
x
DDyxe x−+ =
[JNTU 2001S]
Ans:
22 2
12
()2[2cos2(32)sin2]
xx
yccxe e x xx x=+ +
3.2.2 Linear Equations with Variable Coeffi cients—
Euler–Cauchy Equations (Equidimensional Equations)
An equation of the form
11
01 1
() ( ) ()
nn n n
nn
fxDy axD ax D a xD a y Qx
−−
≡+ +++= (3.80)
or
0
()
n
nr nr
r
r
ax D y Q x
−−
=
⎛⎞
=
⎜⎟
⎝⎠
where
i
a
are all constants and ...
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Publisher Resources

ISBN: 9781299487406Publisher Website