Problem 2. a) Show that y₁ = r5 and y2 = |x5| are linearly independent solutions on the real line of the equation x²y" - 5xy' + 5y = 0. b) Determine the Wronskian W(y1, 92)? Why do these facts do not contradict the theorem stated in class regarding the Wronskian and lincar independence of solutions ?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem 2.
a) Show that y₁ =
x5 and 92
equation x²y" - 5xy' + 5y = 0.
b) Determine the Wronskian W(y1, y2) ? Why do these facts do not contradict the theorem
stated in class regarding the Wronskian and linear independence of solutions ?
-
|x5| are linearly independent solutions on the real line of the
Problem 3.
If y₁ and ₂ are two linearly independent solutions to u" + p(t)y' + g(t)y = 0 (with sav. D
Transcribed Image Text:Problem 2. a) Show that y₁ = x5 and 92 equation x²y" - 5xy' + 5y = 0. b) Determine the Wronskian W(y1, y2) ? Why do these facts do not contradict the theorem stated in class regarding the Wronskian and linear independence of solutions ? - |x5| are linearly independent solutions on the real line of the Problem 3. If y₁ and ₂ are two linearly independent solutions to u" + p(t)y' + g(t)y = 0 (with sav. D
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