||'''Book'''|| Advanced Engineering Mathematics ||
 ||'''Author'''|| Erwin Kreyszig ||
 ||'''Edition'''|| 8th Edition ||

/* code_begins */

{{{
x = var('x')
y = function('y',x) # define y a function of x
DE = x*diff(y,x) - (y-x)^3 - y
print 'DE:';show(DE)

u = function('u',x)
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)

soln = desolve(DE_subs,u,ics=[1,3/2])
soln = soln.subs({u:y/x}) # getting soln back in terms of x and y
sol = solve(soln,y)
print 'Solution:';show(sol)
}}}

/* code_ends */

 * '''Solution by''': 
   * Prashant Agrawal, Student, IIT Bombay