You should do problems involving the exact equation. Here is one example. Solve (2xy + y + 1) + (3xy + 4xy + 3y) dy dx = 0. Solution: Let M(x, y) = 2xy + y + 1 and N(x, y) = 3xy + 4xy + 3y, We have have My = 6xy 2 + 4y and Nx = 6xy 2 + 4y. So My = Nx and the given equation is exact. Thus there is a function φ(x, y) such that φx = M = 2xy +y+1 and φy = N = 3x y+4xy+3y. Integrating the first equa...

In 45,X/46,XY DSDs, the proportion of the two cell lineages is uneven in different organs and tissues, and 45,X and 46,XY cells can be found throughout the body. The gonadal development of 45,X/46,XY patients depends on the population of 46,XY cells in the gonads and the clinical features are variable. We had a 45,X/46,XY DSD patient whose 46,XY population in peripheral blood was extremely low,...

Outbred XY(Sry-) female mice that lack Sry due to the 11 kb deletion Sry(dl1Rlb) have very limited fertility. However, five lines of outbred XY(d) females with Y chromosome deletions Y(Del(Y)1Ct)-Y(Del(Y)5Ct) that deplete the Rbmy gene cluster and repress Sry transcription were found to be of good fertility. Here we tested our expectation that the difference in fertility between XO, XY(d-1) and...

No problem is ever permanently closed. The editor is always pleased to consider for publication new solutions or new insights o n p a s t p r oblems. (1) Determine the set of all c > 0 such that whenever (1) holds, then we have x + y + z xy + yz+ zx. The positive r eals c asked for are those satisfying c 4. From (1), we have xy < c and z = c ; xy x + y + xy. Substituting this value of z into th...

Let F be a field of characteristic zero or of a positive odd characteristic p. For a polynomial f ∈ F[x, y], we define a graph ΓF(xy, f) to be a bipartite graph with vertex partition P ∪L, P = F = L, and (p1, p2, p3) ∈ P is adjacent to [l1, l2, l3] ∈ L if and only if p2 + l2 = p1l1 and p3 + l3 = f(p1, l1). If f = xy, the graph ΓF(xy, xy ) has the length of a shortest cycle (the girth) equal to ...

The results of experimental hybridisation between some chromosome subraces belonging to the X0 and XY chromosome races of the brachypterous grasshopper P. sapporensis are presented. Pre-zygotic reproductive isolation mechanisms in experimental pairs were not confirmed. In crossings of XY-standard x X0-standard and XY-standard x X0-Naganuma chromosome subraces, a zygotic barrier has been found. ...

Given a graph G with vertex set V(G) and edge E(G), for the bijective function f(V(G))?{1,2,?,|V(G)|}, associated weight of an xy?E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, called edge-antimagic labeling. A path P in vertex-labeled said to be rainbow x?y if every two xy,x?y??E(P) it satisfies w(xy)?w(x?y?). The antimagic labeling there exists vertices x,y?V(G)...