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Given an ODE such as $$y''+x^2y'+y=0$$ Is it possible to get sage to display the solution in the from (at least the first few terms of the expansion) $$y=a_o\left(c_0+c_1x+c_2x^2+\dots\right) + a_1\left(d_0+d_1x+d_2x^2+\dots\right) $$

my attempts:

EDIT: I have made some progress, functional but it is not pretty. second attempt

I am writing a worksheet for an ODE course and would like to display the following equation as $$y''+y=1$$ OR as $$\frac{d^2y}{dx^2}+y=1$$ However sage always reverts to partials. Is there an easy way to display these as ordinary differential equations?

thx

see sage cell link text

I can set mu = 0; sigma = 1; P(x)= (1)/(sigma*sqrt(2*pi))*e^((-(x-mu)^2)/(2*sigma^2));

Then I can always get the probability $P( x < z )$ by doing

p=integrate(P,x,-oo,z)

I would like to do the opposite. Given some probability $p_o$ I would like to find the corresponding $z$ so that $P( x < z )=p_0$ I have tried various things.. but keep running into this sort of issue

any help is greatly appreciated

perfect! thank you!

I have this sage cell

x,y,z,t,u,v= var("x,y,z,t,u,v"); f(x,y)=9-x^2-y^2; G=plot_vector_field(f.diff(), (x,-10,10), (y,-10,10), transparent=True, plot_points=12, color="brown", aspect_ratio=1); G.axes_color((0,0,1)); show(G)

but I would like the tick color to match the blue axes color.

all help is appreciated.

I have this so far, but formatting the latex string seems tedious. I am also aware of SageTeX but there, any type of errors simply cause a failure in compiling the pdf file without much information as to what caused the error, or the error messages are not very visible to me. Here is what I have so far.. link text

opacity makes the whole thing transparent. The desired result is as @slelievre points out, to just get rid of the white background. Sorry I can not find anything helpful when I search "transparent" on the docs. Again, thanks for your help.

Plots produced using implicit_plot3d have white background. To get transparent background, I tried using transparent=True in implicit_plot3d and in save, without success:

sage: x, y, z, t = var('x y z t')
sage: name='/Volumes/abcd/Users/efgh/Desktop/ijkl.png'
sage: myplot = implicit_plot3d(z - sqrt(8 - x^2 - y^2),
....:                          [x, -4, 4], [y, -4, 4], [z, -4, 4],
....:                          color='red', axes=True, transparent=True)
sage: myplot.save(filename=name, axes=True, transparent=True, fontsize='12')

The image I obtain has white but not transparent background:

I know implicit_plot3d has an opacity option to set the opacity of the plotted surface, but how can I set the transparency of the background?

I have the following graph and would like to included it on a beamer presentation. It there a way to embed this onto the pdf beamer file? I have sagetex running and working well, works for much of the math on my beamer lectures.

var('x,t,y,t,theta'); @interact def _(degrees=(1..720)): r=4; x=r*(t-sin(t)); y=r*(1-cos(t)); P= point((x.substitute(t=degrees*pi/180), y.substitute(t=degrees*pi/180)), size=80, rgbcolor=(1,0,0)); C = circle((degrees*pi/180*4,4), 4, hue=.7); A = P+C+parametric_plot((x,y), (t,0,degrees*pi/180), rgbcolor=(1,0,0), xmin=-.5, xmax=80, ymin=-1, ymax=10); show(A, xmin=-5.5, xmax=80, ymin=-1, ymax=10)

see link

thank you kindly

thank you, appreciate the sympy tip

f=(e^(-x))/(2+ sin(x));
limit(f,x=infinity)

this yields "undefined", but the limits is clearly zero, thus I gather there's a bug or I am missing something basic . All help is appreciated.

I have

 x,y, dx, dy= var("x, y, dx, dy");
 def iD(f): return diff(f, x)*dx + diff(f,y)*dy;

iD(x^3*y^5) returns

5*dy*x^3*y^4 + 3*dx*x^2*y^5

is there a way to have it return the differentials always at the end as in

5*x^3*y^4*dy + 3*x^2*y^5*dx

thank you

very nice thank you! its perfect!