An Etymological Dictionary of Astronomy and Astrophysics
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A → linear differential equation if the right-hand member is zero, Q(x) = 0, on interval I.

→ homogeneous; → linear; → differential; → equation.

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.

→ linear; → differential; → equation.

A → linear differential equation if Q(x)≠ 0 on interval I.

→ nonhomogeneous; → linear; → differential; → equation.