MATH 240 Midterm: MATH 240 UPenn 240S04 Exams
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In order to receive full credit you need to show all your work . 75: show that the di erential equation (2x+ y 3)dx+ (3xy 2 e 2y)dy = 0 is exact and nd the particular solution with y( 1) = 0, find the general solution to the di erential equation y. 2y + 2y = sin(x: for what values of is every non-zero solution of the di erential equation y. + y + y = 0 unbounded : for what values of does the matrix. 2 1 2 have rank 3 : determine whether the statement is true or false. If true, give a justi cation, if false, give a counterexample. Let a be an n n matrix with distinct positive eigenvalues. Then: det(a) > 0, a is diagonalizable, a is orthogonal, a is symmetric, eigenvectors of a corresponding to distinct eigenvalues are orthogonal, find a basis of eigenvectors for the matrix.
