Problem

Match the differential equations with their slope…

02:14

Problem 1 Easy Difficulty

Match the differential equations with their slope fields, graphed here. (GRAPHS CANNOT COPY)
$$y^{\prime}=x+y$$

Answer

Related Courses

Calculus 2 / BC

University Calculus: Early Transcendentals

Chapter 16

First-Order Differential Equations

Section 1

Solutions, Slope Fields, and Euler’s Method

Discussion

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Video Transcript

Okay. What we want to do is to go ahead and match this differential equation. Why? Prime is equal to X plus why? And we want a match to a slope filled. Okay, so let's not forget what? Why? Prime represents why prime represents the slope. Um uh, any equation or a function, right? The first derivative is a slope of a an equation or function. Um and so what we wanted Teoh is we want to look at the slow field graphs, and what I like to do is I want to look at the slope, feel graphs, and I want to look for horizontal lines. And that is because why prime is going to be zero there, And so for horizontal lines are slope is zero. And so if I'm looking at the slope felines, where is why Prime going to equal zero well is going to be at when x zero, when y zero when x is one. And why has got to be native one? They have to be opposite signs or eggs. His negative one and wise one, or when X is to y has got to be negative, too. They have to be opposite the exact same numerical values, but opposite signs. And so what I'm looking for on that slope field to identify the slope field. I am looking where I have whores on the lines at here. And if this is one negative one So I'm looking for a die ad? No, I di agonal sequence of small whores on the lines. And so the only graph that gives me that is graph de And so that's how it would match up a differential equation to its slope field.

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