Egr 265, math tools for engineering problem solving. Find an explicit solution of the initial value problem y 2x = 2xy, y(1) = 0. It cools down according to newton"s law of cooling in a surrounding medium of temperature 50 f. A mass of 100 kg stretches an undamped spring by 10 cm. Zc xy2 ds, where c is a quarter of a unit circle centered at the origin and contained in the rst quadrant, starting at (1, 0) and ending at (0, 1). A lamina of constant density (x, y) = 1 is bounded by the curves y = x2 and y = 1. (a) find the lamina"s mass. (b) find the lamina"s centroid. Rewrite the function f (x, y) = x + y using polar coordinates and nd its integral over the quarter disk of radius 1 in the rst quadrant.