# [SOLVED]Get WolframAlpha to Plot Slope Fields to DE's

#### Ackbach

##### Indicium Physicus
Staff member
Does anybody (Jester?) know how to get WolframAlpha to plot slope fields to, say, $y'=f(x,y)$? For example, $y'=x^{2}$, and I want the slope field plotted up with $x\in[-2,2]$ and $y\in[-2,2]$. What would the actual command be?

#### Bacterius

##### Well-known member
MHB Math Helper
[JUSTIFY]I think It's VectorPlot. But for some reason WolframAlpha doesn't understand this and just plots dumb topological graphs. Curiously though, if you just ask it "vector plot" it will provide you with configuration options and you can enter your equation/bounds there, but it's a bit awkward to use.[/JUSTIFY]

This works fine under Mathematica 9 though (sorry I typed in the bounds wrong):

Code:
VectorPlot[{x^2, y}, {x, -3, 3}, {y, -3, 3}]

Is this what you mean? Or do you want to differentiate/integrate it first etc..

#### Ackbach

##### Indicium Physicus
Staff member
Yeah, I tried VectorPlot on WA, but it's not giving me what I want. What I want is this sort of thing. This applet is doing what I want, but I'd kind of prefer the safety of WA, if I can get it. I'd rather have short, undirected line segments than the variable length arrows. The problem with the latter is that when the magnitude is small, it's hard to tell in what direction they're pointing.

#### Sudharaka

##### Well-known member
MHB Math Helper
Does anybody (Jester?) know how to get WolframAlpha to plot slope fields to, say, $y'=f(x,y)$? For example, $y'=x^{2}$, and I want the slope field plotted up with $x\in[-2,2]$ and $y\in[-2,2]$. What would the actual command be?

Hi Ackbach,

I doubt whether WolframAlpha supports drawing slope fields. There is a discussion about this in their forums but there's no indication there on how to do this. I used to draw them using Maxima.

Code:
load("plotdf");

plotdf([1,x^2],[x,-2,2],[y,-2,2]);

Yeah, I tried VectorPlot on WA, but it's not giving me what I want. What I want is this sort of thing. This applet is doing what I want, but I'd kind of prefer the safety of WA, if I can get it. I'd rather have short, undirected line segments than the variable length arrows. The problem with the latter is that when the magnitude is small, it's hard to tell in what direction they're pointing.
You might also be interested in the applet posted in the forum thread I have liked above.

Slope Field Calculator

#### Ackbach

##### Indicium Physicus
Staff member
Hi Ackbach,

I doubt whether WolframAlpha supports drawing slope fields. There is a discussion about this in their forums but there's no indication there on how to do this. I used to draw them using Maxima.

Code:
load("plotdf");

plotdf([1,x^2],[x,-2,2],[y,-2,2]);

You might also be interested in the applet posted in the forum thread I have liked above.

Slope Field Calculator
That last one seems pretty good. Thanks for that link!

#### Sudharaka

##### Well-known member
MHB Math Helper
That last one seems pretty good. Thanks for that link!