For dy/dx=x−y, find the slope at (2,1).
Show a complete solution and verify with a second representation.
Unit 12 · Core 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
Core Practice
Differential Equations & Growth Models · Show reasoning, notation, intervals, units, and corrections.
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Date
Solve dy/dx=2y by separation.
Show a complete solution and verify with a second representation.
What does an equilibrium solution require?
Show a complete solution and verify with a second representation.
Verify y=Ce^x solves y'=y.
Show a complete solution and verify with a second representation.
Use y(0)=3 in the previous family.
Show a complete solution and verify with a second representation.
For dy/dx=x−y, find the slope at (2,1).
Show a complete solution and verify with a second representation.
Solve dy/dx=2y by separation.
Show a complete solution and verify with a second representation.
One Euler step for y'=x+y from (0,1) with Δx=0.1.
Show a complete solution and verify with a second representation.
Verify y=Ce^x solves y'=y.
Show a complete solution and verify with a second representation.
Use y(0)=3 in the previous family.
Show a complete solution and verify with a second representation.
What does an equilibrium solution require?
Show a complete solution and verify with a second representation.
Solve dy/dx=2y by separation.
Show a complete solution and verify with a second representation.
One Euler step for y'=x+y from (0,1) with Δx=0.1.
Show a complete solution and verify with a second representation.
For dy/dx=x−y, find the slope at (2,1).
Show a complete solution and verify with a second representation.
Use y(0)=3 in the previous family.
Show a complete solution and verify with a second representation.
What does an equilibrium solution require?
Show a complete solution and verify with a second representation.