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Creating a slope field | First order differential equations | Khan Academy

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Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/e/slope-fields?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/slope-field-to-visualize-solutions?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Missed the previous lesson? https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/finding-particular-linear-solution-to-differential-equation?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Equations channel:: https://www.youtube.com/channel/UCxSQHGkaDv8UKXE0TUbsOIg?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
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Text Comments (21)
Bella (1 month ago)
You explained in 5 minutes what I couldn't understand after a week of classes. Thanks!
joshready (1 month ago)
What does this guy look like? I need to put a face to the voice!
Dolbo (3 months ago)
horrible video actually. he only used easy values: 1's and -1's. should have shown steeper ratios 2/1 3/1 10/1 etc to show how the angle changes to prove the resulting shape of the slope field instead of just making it up "here! it is a circle. done".
Gilbert Keys (9 months ago)
Easiest explanation I've seen
Aaron Alphonsus (1 year ago)
How do I redirect the force of gravity into differential equation slopes that I can surf?
Clay (1 year ago)
Thank you so much for this!
marc kiwan (2 years ago)
You sound like murphy from narcos
Isac Rajan (2 years ago)
Very good explanation. Thank you. :D
Harrison Mohn (2 years ago)
Great video, thanks
Bettina Tobias (2 years ago)
Thank you, Khan Academy for the clear explanation! I have a test on this tomorrow, and this helped me to review. :)
Zara s (3 years ago)
khan is bae
Paperbag Ghost (3 years ago)
that first x you wrote was flawless. lets take a moment and appreciate that x
lollipoplullabies (3 years ago)
Thank you four this! Explained this way better than my book and teacher! ^_^
HD Simplicityy (3 years ago)
Ok...well after trying to learn this in my textbook I sought this video to clarify the basics. I didnt think my book did it well, but this...this helps a lot! Now I need to apply it. Thats the hard part.
Passivly assertive (3 years ago)
Thanks a dozen times
TB (4 years ago)
@Mars TV Channel: -1/0 is not equal to 0. I believe you may be applying the same logic from that of 0/n, to that of n/0. Dividing any kind of number by 0 is undefined. There are interesting videos out there explaining why this is so.  
MARS TV CHANNEL (4 years ago)
How can -1/0 be undefined? It's 0.
Alina C (3 years ago)
Anything over 0 is undefined.
RoyalTrax (4 years ago)
I would love to see some fancy thumbnails on these videos, would drive new user traffic quite a bit (one would imagine).. Thanks Mr. Khan!
Anoir Trabelsi (4 years ago)
After finishing the series on differential equations can you post some real world examples ? Like solving the Schrodinger equation or some other physics differential equations :) Keep it up you're the best 
SnappingEarth (4 years ago)
Love your videos

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