#homework 3
#y1(0)==-0.5
#y2(0)==1
#y3(0)==10
C=var('C')
y=-3/(x^3+C)
show('the equation is',y)
print('when y1(0)=.-5, then C-= 6')
print('when y2(0)=1, then C=-3')
print('when y3(0)=10, then C=-0.3')

y=var('y')
g(x,y)=x^2*y^2
p=plot_slope_field(g(x,y),(x,-15,15),(y,-15,15),headaxislength=3,headlength=3)
p.show()

y1=-3/(x^3+6)
p1= plot(y1, 0, 5, ymin=-15, ymax=15, gridlines='minor', frame= True, color='red')
p1.show()

y2=-3/(x^3-3)
p2= plot(y2, 0, 5, ymin=-15, ymax=15, gridlines='minor', frame= True, color='blue')
p2.show()

y3=-3/(x^3+.03)
p3= plot(y3, 0, 5, ymin=-15, ymax=15, gridlines='minor', frame= True, color='orange')
p3.show()

p4=(p1+p2+p3)
p4.show()

(p+p4).show()

print('the slope field was a summarization of all the graphs and shows the direction in which they will connect and grow')