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Unformatted text preview: MTH205: Review Problems / Final / Fall 05 Q1. Consider the differential equation: x x y y + = ' a) Does the differential equation possess a unique solution through the point ) , ( ? Give reasons. b) Find the general solution, c) Find the solution that satisfies the initial condition 3 ) 1 ( = y , if any. Q2. Classify each of the following differential equations as, separable, exact, linear, homogeneous, or Bernoulli. Then find the general solution of each of them. a) 2 2 2 ' 2 x y xyy = + b) y xy y + = ' c) 2 2 3 2 ' x y xy x y +- = Q3. Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt has been dissolved. Water is pumped into the tank at rate of 1 r gal/min, and then when the solution is well stirred it is pumped out at rate 2 r . Determine a differential equation and solve it for the amount ) ( t x of the salt in the tank at any time t for each of the following cases: a) 4 2 1 = = r r and the entering water is pure. b) 2 , 3 2 1 = = r r and the entering water contains salt with concentration 2 lb/gal....
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- Spring '08