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

/* code_begins */

{{{
# Sec 1.9
# Example 3 
# Picard iteraction
# y'=1+y^2, y(0)=0

var('x')
y = function('y',x)
new_y = function ('new_y',x)
p=[]

y = 0                                    # Initial condition y(0)=0

print 'y( 0 ) is', y

for i in range(4):                            # We calculate 4 iterations   
    new_y = x + integral( y**2 , x , 0 , x )  # By picards Formula, y(n) = x + integral( y(n-1)**2 )
    y=new_y    
    print 'y(',i+1,') is', show(y)
    p.append(plot(y,x,-1,1))
show(sum(p))

}}}

/* code_ends */

 * '''Solution by''': 
   * Aashita Kesarwani, Student, IIT Roorkee
   * <Your Name>, <Profession>, <Organization>