Math 3200 Spring 1997 Test 1
Jan Mandel

In-class, books and notes OK but no calculators please. Number all pages and write your name and the total number of pages on top of page one. Each numbered problem is worth 4 points.

1. For each of the following equations, determine (a) if the equation is ordinary or partial (b) what is the order of the equation (c) if the equation is linear or nonlinear

   

2. 
3. 
4. Verify that is an implicit solution of the equation ydy + xdx = 0.
5. Find the general solution of the differential equation and solve the initial value problem

   , y(0)=1

6. Find the general solution of the differential equation and solve the initial value problem (x+y) dx - x dy = 0, y(1)=1

7. Find the general solution of the differential equation and solve the initial value problem

8. Perform the first two steps of Euler's method with step size h=0.1 for the initial value problem y' = x +y +1, y(0) = 0.

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