Question

linear differential equation with example

Answer 1

Differential equations are equations which have the terms of a dependent variable differentiated only once with respect to an independent variable.

Enough of this high level talk.

Let's be simple and understand.

Any differential equation,
as simple as

dy/dx = 1 is a linear differential equation because it has only y differentiated wrt to x only once.
Another example can be anything like
dy/dx = sinx + tan^2 x - 323
or,

dy/dx = sin^-1 x
or,
dy/dx = 45 sec^2 x tan x sin x

Infinite possible combination

However,

d^2y/dx^2 = 243 sin x isn't a linear differential equation since it has y differentiated wrt x twice

Neither is
d^2x/dt^2 * m = -bdx/dt - kx

a linear differential equation.

Hope it helps you !

Answer 2

Answer:

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,