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P1 Consider the ODE y' = λy + c, with y(0) = 1. a Show that a general step of the second order Taylor Series method for this ODE has the form h² Yn+1 = Yn + h(^yn + C) + (yn + C). 2² b Work out the exact solution of this initial value ODE. c Differentiate your exact solution y(t) from Part 1 b to show that y' (t) = (λ + c)e^t and y'(t) = λ(λ + c)e^t. Is this consistent with your answer to Part 1 a?

P1 Consider the ODE y' = λy + c, with y(0) = 1. a Show that a general step of the second order Taylor Series method for this ODE has the form h² Yn+1 = Yn + h(^yn + C) + (yn + C). 2² b Work out the exact solution of this initial value ODE. c Differentiate your exact solution y(t) from Part 1 b to show that y' (t) = (λ + c)e^t and y'(t) = λ(λ + c)e^t. Is this consistent with your answer to Part 1 a?

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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P1 Consider the ODE y' = λy + c, with y(0) = 1. a Show that a general step of the second order Taylor Series method for this ODE has the form Yn+1 = Yn + h(λ Yn + c) + b Work out the exact solution of this initial value ODE. h² 2^ (^yn + C). c Differentiate your exact solution y(t) from Part 1 b to show that y'(t) = (^ + c)e^t and y'(t) = \(^ + c)e^t. Is this consistent with your answer to Part 1 a?
Transcribed Image Text:P1 Consider the ODE y' = λy + c, with y(0) = 1. a Show that a general step of the second order Taylor Series method for this ODE has the form Yn+1 = Yn + h(λ Yn + c) + b Work out the exact solution of this initial value ODE. h² 2^ (^yn + C). c Differentiate your exact solution y(t) from Part 1 b to show that y'(t) = (^ + c)e^t and y'(t) = \(^ + c)e^t. Is this consistent with your answer to Part 1 a?
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