Search Results for ""

A function used to study ordinary differential equations.

The general nonhomogeneous differential equation is given by x^2(d^2y)/(dx^2)+alphax(dy)/(dx)+betay=S(x), (1) and the homogeneous equation is x^2y^('')+alphaxy^'+betay=0 (2) ...

A second-order partial differential equation of the form Hr+2Ks+Lt+M+N(rt-s^2)=0, (1) where H, K, L, M, and N are functions of x, y, z, p, and q, and r, s, t, p, and q are ...

The system of partial differential equations u_t = b·v_x (1) b_(xt) = u_(xx)b+axv_x-2vx(vxb). (2)

The partial differential equation u_(xxx)-1/8u_x^3+u_x(Ae^u+Be^(-u))=0.

The system of partial differential equations u_t+u_x = v^2-u^2 (1) v_t-v_x = u^2-v^2. (2)

The system of partial differential equations u_t = 3ww_x (1) w_t = 2w_(xxx)+2uw_x+u_xw. (2)

The partial differential equation R[u](u_(rr)+(u_r)/r+u_(zz))=u_r^2+u_z^2, where R[u] is the real part of u (Calogero and Degasperis 1982, p. 62; Zwillinger 1997, p. 131).

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

The partial differential equation u_t=u_(xxx)u^3.