a) Determine the singular point of 2x2(x- 5)²y" + 10xy' + (x² – 25)y = 0 and classify each singular point as regular or irregular.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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a) Determine the singular point of 2x²(x-5)?y" + 10xy' + (x² – 25)y = 0 and
classify each singular point as regular or irregular.
b) Consider the boundary value problem,
a?u a?u
ax2 ' ay?
= 0, 0<x<
o<x< 0<y<
2
0<y<3
u(0, y) = y² – 1, u) = 0, 0<y<
2
u(x.)
= 3x, 0<x<
u(x,0) = 0,
Approximate the solution of the differential equation at the interior points of the
region with mesh size h =
3
c) Find the product solutions for the differential equation uz = -3uyy using separation
of variable method.
z-1
d) Evaluate
dz where C is contour defined by Iz – 3i|
Yz2 + 5z
1/3
Transcribed Image Text:a) Determine the singular point of 2x²(x-5)?y" + 10xy' + (x² – 25)y = 0 and classify each singular point as regular or irregular. b) Consider the boundary value problem, a?u a?u ax2 ' ay? = 0, 0<x< o<x< 0<y< 2 0<y<3 u(0, y) = y² – 1, u) = 0, 0<y< 2 u(x.) = 3x, 0<x< u(x,0) = 0, Approximate the solution of the differential equation at the interior points of the region with mesh size h = 3 c) Find the product solutions for the differential equation uz = -3uyy using separation of variable method. z-1 d) Evaluate dz where C is contour defined by Iz – 3i| Yz2 + 5z 1/3
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