For dy/dx=x−y, find the slope at (2,1).
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 12 · Extended Pathway
Differential Equations & Growth Models
How do differential equations encode change, and how do slope fields and initial conditions determine model behavior?
Khaemenes Academy · Calculus I
Extended Practice
Differential Equations & Growth Models · Show reasoning, notation, intervals, units, and corrections.
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Use y(0)=3 in the previous family.
Generalize, analyze an edge case, or defend the result without relying on technology.
For dy/dx=x−y, find the slope at (2,1).
Generalize, analyze an edge case, or defend the result without relying on technology.
One Euler step for y'=x+y from (0,1) with Δx=0.1.
Generalize, analyze an edge case, or defend the result without relying on technology.
Verify y=Ce^x solves y'=y.
Generalize, analyze an edge case, or defend the result without relying on technology.
One Euler step for y'=x+y from (0,1) with Δx=0.1.
Generalize, analyze an edge case, or defend the result without relying on technology.
Verify y=Ce^x solves y'=y.
Generalize, analyze an edge case, or defend the result without relying on technology.
One Euler step for y'=x+y from (0,1) with Δx=0.1.
Generalize, analyze an edge case, or defend the result without relying on technology.
Verify y=Ce^x solves y'=y.
Generalize, analyze an edge case, or defend the result without relying on technology.
What does an equilibrium solution require?
Generalize, analyze an edge case, or defend the result without relying on technology.
Solve dy/dx=2y by separation.
Generalize, analyze an edge case, or defend the result without relying on technology.
What does an equilibrium solution require?
Generalize, analyze an edge case, or defend the result without relying on technology.