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)
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