MAT 146
Quiz #8 (differential equations) Name
15 points Calculator Used
Impact on Course Grade: approximately 2% Score
Point assignments: 1) 3 pts (2 pts for verification, 1 pt for explanation); 2)2pts (show steps leading to correct value for C); 3)3pts (correct statement of all onstant solutions); 4) 2 pts (accurate and correct sketch); 5)2 pts (accurate and correct table values, including estimate for y(0.2); 6)3pts (all steps leading to solution, stated in the form y=f(x))
Show appropriate evidence to fully support your responses!
1. Verify that , with C a non-zero constant, is a solution to the differential equation . Explain what you have shown.
2. For the situation described in (1), determine the value of the constantCunder the initial condition that y(1)=2.
The slope field of a differential equation is shown to the right. Use it for questions (3) and (4).
3. What are the constant solutions (also known as equilibrium solutions) to the differential equation whose slope field is shown to the right?
4. Given the initial condition that (0,1) satisfies the solution to the differential equation, on the slope field here sketch in the graph of a function that is the particular solution to the differential equation.
5. Complete the table below by using Euler’s Method to determine an approximation for y(0.2), given that and the initial condition thaty(0)=0.
0
1
2 / 0
0.1
0.2 / 0 / 0 / y=0
6. Show the steps of an analytic (symbolic) solution to the separable differentiable equation .