Name:

MATH 285 Section N1
Fall 2001
Quiz 1

Please answer all questions on this sheet. You must show your work to obtain full credit. 10 points are possible. Good luck!

1.

(4 points) Find a function y=f(x) satisfying the initial value problem dy/dx = 6x²-2x; y(1)=3.

2.

(6 points) Consider the initial value problem dy/dx=2y^1/2; y(a)=b.

(a)

For which values of (a,b) is the existence of a solution guaranteed? Explain.

(b)

For which values of (a,b) is there a unique solution? Explain.

(c)

Sketch the direction field as completely as you can, and include in your sketch two distinct solution curves satisfying y(0)=0.