Find the general solution to: $$\frac{dy}{dt}=2t$$

Suppose for a population P(t): the birth rate is constant and equal to 4; the death rate is proportional to P with proportionality constant 2. Write the ODE for \(dP/dt\).

What is the integrating factor \(\rho(x)=e^{{\int P(x)\,dx}}\) for: $$xy’+4y=30$$

The ODE \(y’+\frac{{4}}{{x}}y=x^3\) has integrating factor \(\rho=x^4\). What is the next line in solving the ODE?

Consider \(\frac{dP}{dt}=(P-4)^2(P-10)\). Find all equilibria and classify each.

Find all equilibrium (constant) solutions:\(y” + tyy’ + y^2 = 4\): \(t^2 y” + y’y + 2y = 6t\):

You want to connect from a browser on your laptop to Jupyter running in a container on your VM. What should ???? be in step 3, of the following steps? Step 1: Write a command in the Dockerfile to launch Jupyter on port 2505Step 2: Use -L localhost:4290:localhost:3254 to establish the SSH tunnelStep 3: Use -p ????:2505 in the docker run … commandStep 4: Enter http://localhost:4290/ in the browser

Which of the following is a correctly punctuated compound-complex sentence?

1. (6 points) Use the graph of provided to determine the value of the following limits. If a limit is not infinite and does not exist, write “DNE” as its value.  

5. (8 points) Use the limit definition of the derivative to calculate the derivative of . If you do not use limits to calculate the derivative, you will not earn any credit.