Solve the following problem with the fourth-order RK method: d?y dy +3 dx 2 + 3.125y = sin x dx2 where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5. %3D Find the error considering the exact solution is y(x) = e -0.75x *(5.292237 cos x+6.859589 sin x)-0.292237 cos x+0.109589 sin x Display the analytical and numerical results on the same graph.
Solve the following problem with the fourth-order RK method: d?y dy +3 dx 2 + 3.125y = sin x dx2 where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5. %3D Find the error considering the exact solution is y(x) = e -0.75x *(5.292237 cos x+6.859589 sin x)-0.292237 cos x+0.109589 sin x Display the analytical and numerical results on the same graph.
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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Transcribed Image Text:Solve the following problem with the fourth-order RK method:
d²y
dy
2
+ 3
+ 3.125y = sin x
dx?
dx
where y(0) = 5 and y'(0) = 3. Solve from x = 0 to 5 with h = 0.5.
Find the error considering the exact solution is
y(x) = e
075* (5.292237 cos x+ 6.859589 sin x)-0.292237 cos x+0.109589 sin x
%3D
Display the analytical and numerical results on the same graph.
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