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The Helmholtz differential equation is not separable in bispherical coordinates.

A Fredholm integral equation of the second kind phi(x)=f(x)+lambdaint_a^bK(x,t)phi(t)dt (1) may be solved as follows. Take phi_0(x) = f(x) (2) phi_1(x) = ...

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

The ordinary differential equation y^('')+k/xy^'+deltae^y=0.

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

The second-order ordinary differential equation xy^('')+(c-x)y^'-ay=0, sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

An integral equation of the form f(x)=int_a^xK(x,t)phi(t)dt, where K(x,t) is the integral kernel, f(x) is a specified function, and phi(t) is the function to be solved for.

An integral equation of the form phi(x)=f(x)+int_a^xK(x,t)phi(t)dt, where K(x,t) is the integral kernel, f(x) is a specified function, and phi(t) is the function to be solved ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...