Question
For the following problems, use the direction field below from the differential equation $y^{\prime}=-2 y .$ Sketch the graph of the solution for the given initial conditions.Are there any equilibria? What are their stabilities?
Step 1
This equation tells us that the rate of change of $y$ is proportional to $-2y$. This means that as $y$ increases, the rate of change of $y$ decreases, and vice versa. Show more…
Show all steps
Your feedback will help us improve your experience
Alejandro Ruiz and 99 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
For the following problems, use the direction field below from the differential equation $y^{\prime}=y^{2}-2 y .$ Sketch the graph of the solution for the given initial conditions. Are there any equilibria? What are their stabilities?
Introduction to Differential Equations
Direction Fields and Numerical Methods
For the following problems, use the direction field below from the differential equation $y^{\prime}=-2 y .$ Sketch the graph of the solution for the given initial conditions. $$y(0)=0$$
For the following problems, use the direction field below from the differential equation $y^{\prime}=y^{2}-2 y .$ Sketch the graph of the solution for the given initial conditions. $$y(0)=1$$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD