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An integral equation of the form phi(x)=f(x)+lambdaint_(-infty)^inftyK(x,t)phi(t)dt (1) phi(x)=1/(sqrt(2pi))int_(-infty)^infty(F(t)e^(-ixt)dt)/(1-sqrt(2pi)lambdaK(t)). (2) ...

In two-dimensional Cartesian coordinates, attempt separation of variables by writing F(x,y)=X(x)Y(y), (1) then the Helmholtz differential equation becomes ...

In conical coordinates, Laplace's equation can be written ...

The partial differential equation 1/(c^2)(partial^2psi)/(partialt^2)=(partial^2psi)/(partialx^2)-mu^2psi (1) that arises in mathematical physics. The quasilinear Klein-Gordon ...

The partial differential equation (u_t)/(u_x)=1/4(u_(xxx))/(u_x)-3/8(u_(xx)^2)/(u_x^2)+3/2(p(u))/(u_x^2), where p(u)=1/4(4u^3-g_2u-g_3). The special cases ...

The ordinary differential equation (1) (Byerly 1959, p. 255). The solution is denoted E_m^p(x) and is known as an ellipsoidal harmonic of the first kind, or Lamé function. ...

In conical coordinates, Laplace's equation can be written ...

Partial differential equation boundary conditions which, for an elliptic partial differential equation in a region Omega, specify that the sum of alphau and the normal ...

In three dimensions, the spherical harmonic differential equation is given by ...

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...