122(s08)chapter10sampletest

# 122(s08)chapter10sampletest - b Substance X is converted...

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Name_______________________________ Test III 1.)(7 points) Solve: y t dt dy 3 = 2.) (8 points) Solve: 3 ) 0 ( , ' 2 2 = = - y e t y y 3.) (7 points) Solve: 2 ln ty t dt dy = 4.) (8 points) Solve: 2 ) 0 ( , ' 2 4 2 = - = y y e y y t 5.) (20 points) Given: 7 ) 0 ( 3 ) 0 ( 1 ) 0 ( 4 ) 0 ( 18 3 ' 2 - = - = = = - + = y y y y y y y Sketch the solution of the given differential equation and the initial conditions. Include a yz-graph, label all axes, graphs, and points. 6.) (20 points) a.) A porous material dries outdoors at a rate that is proportional to the moisture content. Set up the differential equation whose solution is y = f(t), the amount of water at time t in a towel on a clothesline. Sketch both the yz-graph and the graph of a solution. Label all graphs.
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Unformatted text preview: b.) Substance X is converted into substance Y at a rate that, at any time t, is proportional to the cube of the amount of X. Set up the differential equation whose solution is y = f(t), the amount of substance X at time t. Sketch both the yz-graph and the graph of the solution. Label all graphs. 7.) (20 points) Use Euler’s method with n = 3 on 1 ≤ ≤ t to approximate the solution f(t) to 9 ) ( , 1 ' = + = y y t y Sketch your solution, label your graph. 8.) (5 points each) Find all constant solutions: a.) 2 3 9 3 ' y y y-= b.) 2 3 yt dt dy =...
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