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1. Assume that p(x), g(x) are continuous functions and that yı (x), y₂(x) satisfy d²y dx² dy +p(x)=+q(x)y(x) = 0. Further, assume that y₁ (x) and y₂ (x) obtain local optima at the same point xo. Show that the Wronskian of y₁ (x) and y2(x) is 0. Hint: What is y₁ (xo)?

1. Assume that p(x), g(x) are continuous functions and that yı (x), y₂(x) satisfy d²y dx² dy +p(x)=+q(x)y(x) = 0. Further, assume that y₁ (x) and y₂ (x) obtain local optima at the same point xo. Show that the Wronskian of y₁ (x) and y2(x) is 0. Hint: What is y₁ (xo)?

Advanced Engineering Mathematics
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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could you help me solute H1 and H2? I dont know how to do.Thanks

H1. Assume that p(x), g(x) are continuous functions and that y₁(x),y₂(x) satisfy d²y dr² Further, assume that y₁ (x) and y2 (x) obtain local optima at the same point.xo. Show that the Wronskian of y₁ (x) and y2(x) is 0. Hint: What is y₁ (xo)? dy •+p(x)=+q(x) y(x) = 0. dx H2. Solve the following differential equation using both the method of undetermined coefficients (trial functions) and the method of variation of parameters d²y dx² dy - 6ªr – 7y = e²¹,y(0) = 3;y′ (0) = 2. dx H3. Solve the following differential equations dy 1) 2) d²y +4+4y=x²e-2x, +9y=e³x (x²+7) dx dy dx
Transcribed Image Text:H1. Assume that p(x), g(x) are continuous functions and that y₁(x),y₂(x) satisfy d²y dr² Further, assume that y₁ (x) and y2 (x) obtain local optima at the same point.xo. Show that the Wronskian of y₁ (x) and y2(x) is 0. Hint: What is y₁ (xo)? dy •+p(x)=+q(x) y(x) = 0. dx H2. Solve the following differential equation using both the method of undetermined coefficients (trial functions) and the method of variation of parameters d²y dx² dy - 6ªr – 7y = e²¹,y(0) = 3;y′ (0) = 2. dx H3. Solve the following differential equations dy 1) 2) d²y +4+4y=x²e-2x, +9y=e³x (x²+7) dx dy dx
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