• Book	Advanced Engineering Mathematics
  Author	Erwin Kreyszig
  Edition	8th Edition

code_begins

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())

code_ends

# 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