# Differential-equation Sentence Examples

differential-equation
• Since dp4+(-)P+T1(p +q qi 1)!dd4, the solutions of the partial differential equation d P4 =o are the single bipart forms, omitting s P4, and we have seen that the solutions of p4 = o are those monomial functions in which the part pq is absent.

• He also showed that every equation of an even degree must have at least one real quadratic factor, reduced the solution of linear differential equations to definite integrals, and furnished an elegant method by which the linear partial differential equation of the second order might be solved.

• The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

• The other method starts from the observed values of the periods, and establishes a differential equation from which these periods may be derived.

• Riecke, 3 who deduced a differential equation of the 10th order.

• Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.

• We thus obtain the differential equation gk(d 2 0/dx 2) =cgdo/dt+hpo, which is satisfied by terms of the type =c" sin where a 2 -b 2 = hp/qk, and ab = urnc/k.

• The differential equation for the distribution of temperature in this case includes the majority of the methods already considered, and may be stated as follows.

• His well-known correction of Laplace's partial differential equation for the potential was first published in the Bulletin de la societe philomatique (1813).

• If in this we put r= I/u, and eliminate t by means of (15), we obtain the general differential equation of central orbits, viz.