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Course: ME 302, Spring 2008School: Cal Poly
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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Cal Poly - ME - 302
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UCLA - MATH - 33B
Math 33b, Quiz 1ac, January 15, 2008 Name: UCLA ID:1. Using any technique possible, find the solution to the initial-value problem 2 1 dy y + = 2 , y(1) = 4. dx x xSolution. We can rewrite this equation as a linear differential equation: 1 1 dy +
UCLA - MATH - 33B
Math 33b, Quiz 1bd, January 17, 2008 Name: UCLA ID:1. Using any technique possible, find the solution to the initial-value problem 4x dy + 2 y = 1, y(0) = -2. dx x + 1 Solution. The differential equation is linear, so we want to multiply both sides
UCLA - MATH - 33B
Math 33b, Quiz 2ac, January 22, 2008 Name: UCLA ID:1. Find the general solution to the initial-value problem (x2 + xy 3 )dx + (-3x2 y 2 )dy = 0, y(1) = 8. (An integrating factor of the form (x) will be required to make the given equation exact.) So
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Math 33b, Quiz 2bd, January 24, 2008 Name: UCLA ID:1. A tank initially containing 100 gallons of pure water is being fed by a pipe which pours in a solution at the rate of 2 gallons per minute. The solution contains 0.5 pounds of salt per gallon. A
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Math 33b, Quiz 3ac, January 29, 2008 Name: UCLA ID:1. Consider a lake that is being used as a fish farm; here fish are raised and eventually sold for food. The population of the lake is given by y = ry(1 - y/K) - h, where r, K, h are constants. Her
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Math 33b, Quiz 3bd, January 30, 2008 Name: UCLA ID:1. Consider a lake that is being used as a fish farm; here fish are raised and eventually y sold for food. The population of the lake is given by y = ry(1 - K ) - h, where r, K, h are constants. He
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Math 33b, Quiz 4ac, February 5, 2008 Name: UCLA ID:1. Find the general solution to the differential equation y - 3y - 10y = e-2t . Solution. The general solution y(t) is of the form y = yh + yp , where yh is a solution to the homogeneous equation y
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Math 33b, Quiz 4bd, February 7, 2008 Name: UCLA ID:1. Find the general solution to the differential equation y - 2y + y = sin 4t. Solution. The solution has the form y = yh + yp , where yh is the solution to the homogeneous equation y -2y +y = 0 an
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Math 33b, Quiz 5ac, February 26, 2008 Name: UCLA ID:1. Find the solution with initial conditions y(0) = 0, y (0) = 0 to the differential equation y +y = 1, 0t<3 -2(t-3) e , t 3.Solution. Observe that the function f (t) on the right-hand-side of
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Math 33b, Quiz 5bd, February 28, 2008 Name: UCLA ID:1. Find the solution with initial conditions y(0) = 0, y (0) = 0 to the differential equation y +y = t, 0t<1 cos 2(t - 1), t 1.(A small table of Laplace transforms is on the back of the quiz.)
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Math 33b, Quiz 6ac, March 4, 2008 Name: UCLA ID: 2 , to the system of differential 31. Find the solution, with initial condition x(0) = equations dx = dt -1 -1 x. 4 -5-1 - -1 , 4 -5 - which is 2 + 6 + 9. The roots are = -3, -3, so there is onl
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Math 33b, Quiz 6bd, March 6, 2008 Name: UCLA ID: 2 , to the system of differential 41. Find the solution, with initial condition x(0) = equations dx = dt 2 1 x. -5 42- 1 , which is -5 4 - 2 - 6 + 13. The roots of this polynomial are 3 2i, so th
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Math 33b, Quiz 7ac, March 11, 2008 Name: UCLA ID:Consider the system of differential equations x (t) = Mx, where M is each of the matrices below. For each system of differential equations, a sample solution in the x-y plane is plotted below. Below
UCLA - MATH - 33B
Math 33b, Quiz 7bd, March 12, 2008 Name: UCLA ID:Consider the system of differential equations x (t) = Mx, where M is each of the matrices below. For each system of differential equations, a sample solution in the x-y plane is plotted below. Below
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