Math 33b, Quiz 2bd, April 19, 2007 Name: UCLA ID:
1. Find the general solution to the differential equation (2x2 + xy 3 )dx + (3x2 y 2 )dy = 0. (An integrating factor of the form (x) will be required to make the given equation exact.) Solution. Set
Math 33b, Quiz 5bd, May 24, 2007 Name: UCLA ID:
1. Find the general solution to the system of differential equations dx = dt -4 5 x. -1 -2 -4 5 -1 -2 by solving the
Solution. First we find the eigenvalues of the matrix A = characteristic equation:
Math 33b, Quiz 4bd, May 3, 2007 Name: UCLA ID:
1. Find the general solution to the differential equation y + 2y + y = sin 3t. Solution. The general solution y(t) is of the form y = yh + yp , where yh is the general solution to the homogeneous equati
Math 33b, Quiz 3bd, April 26, 2007 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. Here