Slope Fields Calculator

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Example

Created on 2024-06-20Asked by William Flores (Solvelet student)

Sketch the slope field for the differential equation

\frac{dy}{dx} = x - y

Solution

\ To sketch the slope field for the differential equation

\frac{dy}{dx} = x - y

: 1. **Create a grid of points

(x, y)

:** Choose points

(x, y)

on a grid, for example,

-2 \leq x, y \leq 2

. 2. **Compute the slope at each point:** At each point

(x, y)

, the slope is

x - y

. 3. **Draw small line segments with the computed slopes:** Use a software tool or manually sketch the line segments. \begin{tikzpicture} \begin{axis}[ axis equal, xlabel={

x

}, ylabel={

y

}, xmin=-2, xmax=2, ymin=-2, ymax=2, samples=15, domain=-2:2] \addplot[quiver={u=\thisrow{u}, v=\thisrow{v}}, blue] table { x y u v -2 -2 0 -2 -2 -1 1 -1 -2 0 2 0 -2 1 3 1 -2 2 4 2 -1 -2 1 -3 -1 -1 2 -2 -1 0 3 -1 -1 1 4 0 -1 2 5 1 0 -2 2 -4 0 -1 3 -3 0 0 4 -2 0 1 5 -1 0 2 6 0 1 -2 3 -5 1 -1 4 -4 1 0 5 -3 1 1 6 -2 1 2 7 -1 2 -2 4 -6 2 -1 5 -5 2 0 6 -4 2 1 7 -3 2 2 8 -2 }; \end{axis} \end{tikzpicture} Solved on Solvelet with Basic AI Model

Some of the related questions asked by Logan Sanchez on Solvelet

1. Sketch the slope field for the differential equation

\frac{dy}{dx} = x + y

.2. Given the slope field for the differential equation

dy/dx = 2x - y

, determine the solution passing through the point

(0, 1)

DefinitionIn mathematics slope fields, also known as taccion fields, are the way of graphically representing first order differential equations. These are tiny line segments on the grid points which represent a slope of the solution curve at this point. Ex: (y-5)*dy/d. dx - slope field shows how the slope changes with respect to x and y;

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