Solve the given ODE using the power series method. y' – xy = 0 -

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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Solve the given ODE using the power series method.
y' – xy = 0
2.
Obtain the recurrence relation.
- ag – 1
as+1
s + 1
O as+1
s + 1
as –1
O as+1
s + 1
- as
a s+1
s + 1
3.
Determine the general solution. Write the first six terms of the series.
„4
+
8
x2
y = ao(1+
2
...
x2
+
2!
= ao( 1+ x +
+
...
3!
x2
1
y = ao
2
+
8
y = ao( 1 – x +
2!
+
3!
+
Transcribed Image Text:Solve the given ODE using the power series method. y' – xy = 0 2. Obtain the recurrence relation. - ag – 1 as+1 s + 1 O as+1 s + 1 as –1 O as+1 s + 1 - as a s+1 s + 1 3. Determine the general solution. Write the first six terms of the series. „4 + 8 x2 y = ao(1+ 2 ... x2 + 2! = ao( 1+ x + + ... 3! x2 1 y = ao 2 + 8 y = ao( 1 – x + 2! + 3! +
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