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In two-dimensional bipolar coordinates, Laplace's equation is ((coshv-cosu)^2)/(a^2)((partialF^2)/(partialu^2)+(partialF^2)/(partialv^2))=0, which simplifies to ...

The ordinary differential equation y^('')+(1-|y|)y^'+y=0.

The system of ordinary differential equations X^. = sigma(Y-X) (1) Y^. = rX-Y-XZ (2) Z^. = XY-bZ. (3)

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 ...

Partial differential equation boundary conditions which give the normal derivative on a surface.

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.

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

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

C=tauT+kappaB, where tau is the torsion, kappa is the curvature, T is the tangent vector, and B is the binormal vector.