Ecuaciones Diferenciales exactas

x,y = var("x,y")
M(x,y) = 2*x*y
N(x,y) = 1+x^2
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = x^2*y+y

R = 1
intervalo_x = (x,-R,R)
intervalo_y = (y,-R,R)


campo = contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="red")
campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")
campo.show(gridlines=True)
campo.save('./images/0218a.png',aspect_ratio=1)

superficie = plot3d(g(x,y), intervalo_x, intervalo_y, adaptive=True, color=rainbow(60, 'rgbtuple'))
superficie.show()
superficie.save('./images/0218b.png')

x,y = var("x,y")
M(x,y) = y
N(x,y) = -x
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = y/x

R = 1
intervalo_x = (x,-R,R)
intervalo_y = (y,-R,R)

cm = colormaps.jet
def c(x,y): return (y/x+100)/200


campo = contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="red")
campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")
campo.show(gridlines=True)
campo.save('./images/0219a.png',aspect_ratio=1)

x,y = var("x,y")
M(x,y) = x+sin(y)
N(x,y) = x*cos(y)-2*y
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = x^2/2+x*sin(y)-y^2

R = 1
intervalo_x = (x,-R,R)
intervalo_y = (y,-R,R)


campo = contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="red")
campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")
campo.show(gridlines=True)
campo.save('./images/0220a.png',aspect_ratio=1)

superficie = plot3d(g(x,y), intervalo_x, intervalo_y, adaptive=True, color=rainbow(60, 'rgbtuple'))
superficie.show()
superficie.save('./images/0220b.png')

x,y = var("x,y")
M(x,y) = 2+y*exp(x*y)
N(x,y) = -2*y+x*exp(x*y)
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = 2*x+exp(x*y)-y^2

R = 2
intervalo_x = (x,-R,R)
intervalo_y = (y,-R,R)


campo = contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="red")
campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")
campo.show(gridlines=True)
campo.save('./images/0221a.png',aspect_ratio=1)

cm = colormaps.jet
def c(x,y): return (2*x+exp(x*y)-y^2+8)/56

superficie = plot3d(g(x,y), intervalo_x, intervalo_y, adaptative=True, color=(c,cm))
superficie.show()
superficie.save('./images/0221b.png')

x,y = var("x,y")
M(x,y) = y^2
N(x,y) = 2*y*x+1
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = y^2*x+y

R = 2
intervalo_x = (x,-R,R)
intervalo_y = (y,-R,R)


campo = contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="red")
campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")
campo.show(gridlines=True)
campo.save('./images/0222a.png',aspect_ratio=1)

cm = colormaps.jet
def c(x,y): return (y^2*x+y+10)/20

superficie = plot3d(g(x,y), intervalo_x, intervalo_y, adaptative=True, color=(c,cm))
superficie.show()
superficie.save('./images/0222b.png')

x,y = var("x,y")
M(x,y) = y^2
N(x,y) = 2*y*x+1
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = y^2*x+y

R = 5
intervalo_x = (x,1-R,1+R)
intervalo_y = (y,-2-R,-2+R)

campo = Graphics()
campo += contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True, contours=20)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="red")
campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")
campo += implicit_plot(g(x,y)-2, intervalo_x, intervalo_y, color="purple", linewidth=3)
campo.show(gridlines=True)
campo.save('./images/0223.png',aspect_ratio=1)

x,y = var("x,y")
M(x,y) = y
N(x,y) = -x
f(x,y) = -M(x,y)/N(x,y)
v = [M(x,y),N(x,y)]
g(x,y) = y/x

R = 1
intervalo_x = (x,-R,R)
intervalo_y = (y,-R,R)

cm = colormaps.jet
def c(x,y): return (y/x+100)/200

campo = Graphics()
#campo = contour_plot(g(x,y), intervalo_x, intervalo_y, cmap="jet",  colorbar=True)
campo += plot_vector_field(v, intervalo_x, intervalo_y, color="purple")
#campo += plot_slope_field(f, intervalo_x, intervalo_y, color="blue")

from numpy import arange
for a in linspace(-180,180,45):
    r = (a/180)*pi
    m = tan(r)
    col = (m+10)/20
    campo += implicit_plot(y-m*x, intervalo_x, intervalo_y, color=hue(col))

campo.show(gridlines=True)
campo.save('./images/0224.png',aspect_ratio=1)