Find two power series solutions of the given differential equation about the ordinary point x = 0. y"-5xy+ y = 0 3x 21 19x5 Y=1- and Yz = x = x³ + 4x° 52x 8. 80 105 Y =1+ 11x 77x5 and y = x + x²- 4x 52x 24 240 105 Y1 = 1- 3x 19x5 2x and y = x + 4x 80 3 15 15 3x8 Y1 =1- 19x12 2x5 and y, = x + 7x9 4x3 80 3. 15 15 11x 77x6 Y = 1+ 2 2x and y = x + 7x 4x 24 240 15 15 00

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find two power series solutions of the given differential equation about the ordinary point x = 0.
y" - Sxy + y = 0
O y, = 1-
3x
19x6
4x
52x
and y, = x + x
80
5
105
O Y1 = 1+ , llx*
2
77x5
and y, = x + x +
52x
24
240
105
O y, = 1-
3x4
19x5
and y. = x + 2X
7x
4x
80
3
15
15
Y = 1-
19x12
7x
and y, = x + 2x°
3
4x13
80
15
15
11x
77x6
2x3
どら x+
3
and
7x5
4x
24
240
15
15
Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0. y" - Sxy + y = 0 O y, = 1- 3x 19x6 4x 52x and y, = x + x 80 5 105 O Y1 = 1+ , llx* 2 77x5 and y, = x + x + 52x 24 240 105 O y, = 1- 3x4 19x5 and y. = x + 2X 7x 4x 80 3 15 15 Y = 1- 19x12 7x and y, = x + 2x° 3 4x13 80 15 15 11x 77x6 2x3 どら x+ 3 and 7x5 4x 24 240 15 15
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