Search Results for ""

The second-order ordinary differential equation (Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 166).

The system of partial differential equations u_t = 1/2u_(xxx)+3uu_x-6ww_x (1) w_t = -w_(xxx)-3uw_x. (2)

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

The ordinary differential equation y^'=-y(1+kappa(x)y)/(1-kappa(x)y).

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

The partial differential equation u_t=del ·(u^mdel u).

The ordinary differential equation y^('')+(lambda-x^(2n))y=0.

The partial differential equation 3/4U_y+W_x=0, (1) where W_y+U_t-1/4U_(xxx)+3/2UU_x=0 (2) (Krichever and Novikov 1980; Novikov 1999). Zwillinger (1997, p. 131) and Calogero ...

y=x(dy)/(dx)+f((dy)/(dx)) (1) or y=px+f(p), (2) where f is a function of one variable and p=dy/dx. The general solution is y=cx+f(c). (3) The singular solution envelopes are ...