Solve the following differential equation (by hand, on paper) dy=x-² dx where y(1) = 1 _ (x³ +c)¸ solve for c. 3x a) Given that the analytical solution is y=- Then for a step size h = Ax=0.2: b) Modified Euler's Method for two steps (predictor corrector). c) Using fourth-order Runge-Kutta for two steps. d) How do these compare to the exact value at x = 1.4?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Solve the following differential equation (by hand, on paper)
dy
dx
X
X
where y(1) = 1
(x³ + c)
3x
a) Given that the analytical solution is y=-
solve for c.
Then for a step size h = Ax = 0.2:
b) Modified Euler's Method for two steps (predictor corrector).
c) Using fourth-order Runge-Kutta for two steps.
d) How do these compare to the exact value at x = 1.4?
Transcribed Image Text:2. Solve the following differential equation (by hand, on paper) dy dx X X where y(1) = 1 (x³ + c) 3x a) Given that the analytical solution is y=- solve for c. Then for a step size h = Ax = 0.2: b) Modified Euler's Method for two steps (predictor corrector). c) Using fourth-order Runge-Kutta for two steps. d) How do these compare to the exact value at x = 1.4?
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