Find two power series solutions of the given differential equation about the ordinary point x = 0. у" + ху = 0 ,3 4 = x + 12 x' Y, = 1 + 6 and Y2 180 504 .3 O Y1 4 + 12 = 1 + x2 and y, = x + x² + ,2 + 2 4 O Y1 = 1 and Y2= X - 24 120 .3 4 O Y1* x7 + = 1 and = X - 6 180 12 504 x2 + 2 24 4 x3 x5 O Y1 = 1 + and y, = xX + + + 6 120 + ...
Find two power series solutions of the given differential equation about the ordinary point x = 0. у" + ху = 0 ,3 4 = x + 12 x' Y, = 1 + 6 and Y2 180 504 .3 O Y1 4 + 12 = 1 + x2 and y, = x + x² + ,2 + 2 4 O Y1 = 1 and Y2= X - 24 120 .3 4 O Y1* x7 + = 1 and = X - 6 180 12 504 x2 + 2 24 4 x3 x5 O Y1 = 1 + and y, = xX + + + 6 120 + ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0.
у" + ху 3D0
x3
x7
+
4
O Y1
= 1 +
and
= x +
12
+
Y2
6
180
504
x3
+ ...
+
6
4
O Y1
= 1 + x2
and
= x + x2
+
+
12
x5
+
4
.3
O y, = 1
Y =
and
Y2 =
+
X -
24
6.
120
O y1 = 1
x
+
x4
x'
+
and y, 3D х —
=
180
12
504
2
1 +
.3
x
Y, = x +
4
O y1 =
+
and
+
+
...
24
6.
120
+
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