Problem 2. a) If y₁ is a known nonvanishing solution to y" +p(t)y' + q(t)y = 0, show that a second solution y2 satisfies (y2/91)' = W(y1, 92)/y, where W(y1, 92) is the Wronskian of Yı and Y2. Then use Problem 1, to determine y2 (as a function of y₁). b) Check that y₁ (t) = t¹ is a solution to t²y" + 3ty' + y = 0 (t > 0). Find a second solution, linearly independent to y₁.
Problem 2. a) If y₁ is a known nonvanishing solution to y" +p(t)y' + q(t)y = 0, show that a second solution y2 satisfies (y2/91)' = W(y1, 92)/y, where W(y1, 92) is the Wronskian of Yı and Y2. Then use Problem 1, to determine y2 (as a function of y₁). b) Check that y₁ (t) = t¹ is a solution to t²y" + 3ty' + y = 0 (t > 0). Find a second solution, linearly independent to y₁.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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