Book
Advanced Engineering Mathematics
Author
Erwin Kreyszig
Edition
8th Edition
x = var('x') # define a variable x
y = function('y',x) # define y to be a function of that variable
DE = diff(y,x)*cosh(x)^2 - sin(y)^2 == 0
print 'Differential Equation:'
show(DE)
soln = desolve(DE, [y,x])
print 'Solution:'
show(soln)
print 'Explicit solution:'
esoln = soln.solve(y)
esoln
inc_simp = (soln.solve(y)[0].rhs().subs(x=0)==pi/2)
inc_simp
simp = 1/tan(inc_simp).simplify_full()
simp
c = solve(simp,soln.variables()[0])
print 'Integration constant:'
show(c)
print 'Explicit solution:'
esoln[0].subs(c=c[0].rhs())
# Notes: desolve sometimes cannot solve the DE if ics (initial conditions) are given, but can solve it if they are not given. This shouldn't be the case, since it is simply a direct substitution
Solution by:
- Pankaj Pandey, Student, IIT Bombay