An Etymological Dictionary of Astronomy and Astrophysics

An equation in which the → dependent variable y and all its differential coefficients occur only in the first degree. A linear differential equation of → order  order n has the form:
f_n(x)y⁽ⁿ⁾ + f_n-1(x)y^(n-1) + … + f₁(x)y^’ + f₀(x)y = Q(x),

where f₀(x), f₁(x), …, f_n(x) and Q(x) are each continuous functions of x defined on a common interval I and f_n(x)≠ 0 in I. A linear differential equation cannot have, for example, terms such as y² or (y^’)^1/2. See also:
→ homogeneous linear differential equation; → nonhomogeneous linear differential equation.

See also: → linear; → differential; → equation.