Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - 3xy' + y = 0 +... and y, = x+** 15 2x5 2x? + 91x5 + *... 2 24 720 3 45 x* 5x3 and y; = x ++. 2x°, 2x13 11x12 O y, = 1. + 24 144 15 45 x² . 7x* 91x5 x* . 8x7 O y, = 1+ 2 +... and y, = x + + + + + 24 720 3 63 x2 Y, =1- 5x* 11x5 and Y2 = x3 2x. 2x7 + 24 144 15 45 x2 O y, = 1 2x. x, 8x7 11x5 and Y2= = x + 3 + 24 144 63

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I dont undertstand how to get the y2 portion of the problem which includes x^3/3 and 2x^5/15

Find two power series solutions of the given differential equation about the ordinary point x = 0.
у" - Зху + у - о
x2
7x*
+
91x5
+
x. 2x5. 2x7
and y, = x +.
3
= 1 +
+...
+
+
+
2
24
720
15
45
O y, = 1
11x12
2x9
+
2x13
and y, = x +
2
24
144
15
45
O y, = 1+
x2
7x*
91x5
2x , x5
8x7
+
+
and y, = x +
+...
24
720
63
x2
Y = 1-
5x4
11x5
x3
= x +
2x5
+
+
2x7
+
and
Y2
-
...
24
144
15
45
and y,- .
O y, = 1
x2
5x4
11x5
2x
= x +
8x7
+
-
Y2
24
144
3
63
+
Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0. у" - Зху + у - о x2 7x* + 91x5 + x. 2x5. 2x7 and y, = x +. 3 = 1 + +... + + + 2 24 720 15 45 O y, = 1 11x12 2x9 + 2x13 and y, = x + 2 24 144 15 45 O y, = 1+ x2 7x* 91x5 2x , x5 8x7 + + and y, = x + +... 24 720 63 x2 Y = 1- 5x4 11x5 x3 = x + 2x5 + + 2x7 + and Y2 - ... 24 144 15 45 and y,- . O y, = 1 x2 5x4 11x5 2x = x + 8x7 + - Y2 24 144 3 63 +
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