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y=x(dy)/(dx)+f((dy)/(dx)) (1) or y=px+f(p), (2) where f is a function of one variable and p=dy/dx. The general solution is y=cx+f(c). (3) The singular solution envelopes are ...

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

The word differential has several related meaning in mathematics. In the most common context, it means "related to derivatives." So, for example, the portion of calculus ...

A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

A functional differential equation is a differential equation in which the derivative y^'(t) of an unknown function y has a value at t that is related to y as a function of ...

(1) or (2) The solutions are Jacobi polynomials P_n^((alpha,beta))(x) or, in terms of hypergeometric functions, as y(x)=C_1_2F_1(-n,n+1+alpha+beta,1+alpha,1/2(x-1)) ...

A delay differential equation (also called a differential delay equation or difference-differential equation, although the latter term has a different meaning in the modern ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

The Abel equation of the first kind is given by y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+... (Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second ...