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⇤ ← Revision 1 as of 2010-08-09 14:02:56
Size: 666
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← Revision 2 as of 2010-08-09 14:03:19 ⇥
Size: 651
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| Deletions are marked like this. | Additions are marked like this. |
| Line 14: | Line 14: |
| DE_subs = DE.subs({y:x*u,diff(y,x):diff(x*u,x)}) # substituting y/x as u print 'DE substituted:';show(DE_subs) |
DE = DE.subs({y:x*u,diff(y,x):diff(x*u,x)}) # substituting y/x as u print 'DE substituted:';show(DE) |
| Line 17: | Line 17: |
| soln = desolve(DE_subs,u,ics=[1,pi]) | soln = desolve(DE,u,ics=[1,pi]) |
Book
Advanced Engineering Mathematics
Author
Erwin Kreyszig
Edition
8th Edition
x = var('x')
y = function('y',x) # define y a function of x
DE = x*diff(y,x) - y - x^2*sec(y/x)
print 'DE:';show(DE)
u = function('u',x)
DE = DE.subs({y:x*u,diff(y,x):diff(x*u,x)}) # substituting y/x as u
print 'DE substituted:';show(DE)
soln = desolve(DE,u,ics=[1,pi])
soln = soln.subs({u:y/x}) # getting soln back in terms of y and x only
sol = solve(soln,y)
print 'Solution:';show(sol)
Solution by:
- Prashant Agrawal, Student, IIT Bombay