linear differential equation

American  

noun

Mathematics.

1. an equation involving derivatives in which the dependent variables and all derivatives appearing in the equation are raised to the first power.

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Etymology

Origin of linear differential equation

First recorded in 1885–90

Example Sentences

Prove that if a, b, and c are positive constants, then all solutions to the second-order linear differential equation ay″ + by′ + cy = 0 approach zero as x → ∞.

From Textbooks • Mar. 30, 2016

We will use it later when finding the solution to a general first-order linear differential equation.

From Textbooks • Mar. 30, 2016

We can use a five-step problem-solving strategy for solving a first-order linear differential equation that may or may not include an initial value.

From Textbooks • Mar. 30, 2016

This leads to a general method for solving a first-order linear differential equation.

From Textbooks • Mar. 30, 2016

A differential equation of this form is satisfied by the quotient of two independent integrals of the linear differential equation of the second order satisfied by the hypergeometric functions.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" by Various