Search Results for ""

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

The partial differential equation u_(yy)=yu_(xx).

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.

(dy)/(dx)+p(x)y=q(x)y^n. (1) Let v=y^(1-n) for n!=1. Then (dv)/(dx)=(1-n)y^(-n)(dy)/(dx). (2) Rewriting (1) gives y^(-n)(dy)/(dx) = q(x)-p(x)y^(1-n) (3) = q(x)-vp(x). (4) ...

A boundary value problem is a problem, typically an ordinary differential equation or a partial differential equation, which has values assigned on the physical boundary of ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

The partial differential equation (1+f_y^2)f_(xx)-2f_xf_yf_(xy)+(1+f_x^2)f_(yy)=0 (Gray 1997, p. 399), whose solutions are called minimal surfaces. This corresponds to the ...

When A and B are self-adjoint operators, e^(t(A+B))=lim_(n->infty)(e^(tA/n)e^(tB/n))^n.

An Anosov diffeomorphism is a C^1 diffeomorphism phi of a manifold M to itself such that the tangent bundle of M is hyperbolic with respect to phi. Very few classes of Anosov ...

The bifurcation of a fixed point to a limit cycle (Tabor 1989).