aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa MATH 20D - Practice Exam #1 The exam covers Sections 1.1-3.2 (inclusive) minus 2.8 and 2.9 closed book, no calculators, no computers, no notes, no headphones . .. each problem is worth the same number of points aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa 1) a) Find an integrating factor u for y’ - xy = -x. b) Solve the ODE in part a) by multiplying it by the integrating factor u and recognizing the left hand side as (uy)’. 2) Solve the separable ODE y y’ + x = 0 with initial condition y(2)=2. Find the interval a ≤ x ≤ b where the solution y(x) is defined. If you were to plot the direction field, what would you expect to see? 3) A tank contains 100 gallons of salty water made by dissolving 80 lb. of salt in water. Pure water runs into the tank at the rate of 4 gal./min, and the well-stirred mixture runs out at the same rate. Let Q(t) be the amount of salt in the tank at time t. a)
This is the end of the preview.
access the rest of the document.
Boundary value problem, Lipschitz continuity