Solution of the form
Show that the following equation has a solution of the form u(x,y) = e^(ax+by). Find the constants a and b: u_xx + u_yy = 5e^(x-2y)
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In the US Senate, each of 100 Senators has one vote, and vice president of US can vote also if it is necessary to break tie. If simple majority is required to pass a bill, what constitutes a winning coalition, and what constitutes a blocking coal
Determine an example of a family {Un : n is an element of N} of open sets of R for which the intersection from n=1 to infinity Un is not open.
Carry out eulers method twice to approximate to this solution on interval [0, 0.5], first with step size h = 0.25, then with step size h = 0.1. Compare the three decimal-place values of the two approximations at x = 0.5 with the value y(0.5) of th
A copper pipe, employed for plumbing from the water main to a house, is 5 meters long and has a circular cross-section 2.8 cm in diameter. There is a 2 cm diameter hole in the center of the cross-section for the entire length of the rod. What is
The following data can be employed to approximate the integral: M = ?3? ÷ 2 0 cos x dx N1(h) = 2.356194 N1(h ÷ 2) = -0.4879837 N1(h ÷ 4) = -0.8815732 N1(h ÷ 8) = -0.9709157 Suppose a formula exists of the type given in
Find out whether the given differential equation is exact. If it is exact, solve it. (y ln y ? e?xy) dx + (1/y + x ln y) dy = 0.
Find the value of k so that the given differential equation is exact. (y^3 + kxy^4 ? 2x) dx + (3xy^2 + 24x^2(y^3)) dy = 0.
Prove the following Theorem. If (X,d) is a metric space, then there is bounded metric on X which is equivalent to d. recall: When we say a metric p is bounded, we mean that there exists an M >0 such that p(x,y) <= M for all x,y in X.
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