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The general equation of fluid flow (lambda+2mu)del (del ·u)-mudel x(del xu)=rho(partial^2u)/(partialt^2), where mu and lambda are coefficients of viscosity, u is the velocity ...

The functional equation phi(f(x))=sphi(x), with s!=0,1.

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

The partial differential equation ((partial^2)/(partialt^2)-(partial^2)/(partialx^2))((u_(xy))/u)+2(u^2)_(xt)=0.

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...

The second-order ordinary differential equation y^('')+g(y)y^('2)+f(x)y^'=0 (1) is called Liouville's equation (Goldstein and Braun 1973; Zwillinger 1997, p. 124), as are the ...

A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

sum_(i=1)^n((partialu)/(partialx_i))^2=1.

dtau^2=-eta_(alphabeta)dxi^alphadxi^beta, or (d^2xi^alpha)/(dtau^2)=0.

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