A linear differential equation is of differential equation which can be written in the subsequent form.

a_n(t) y⁽ⁿ⁾ (t) + a _n-1 (t) y^(n-1) (t)+..............+ a₁(t) y'(t) + a₀ (t) y(t) = g (t)

The significant thing to note regarding linear differential equations is as there are no products of the function, y(t), and its derivatives and neither the function nor its derivatives arise to any power other than the first power.

The coefficients a₀ (t),.........,a_n (t) and g (t) can be zero or non-zero functions, constant or non-constant functions, linear or non-linear functions. Merely the function, y (t), and its derivatives are employed in finding if a differential equation is linear.

If a differential equation can't be written in form, equation (11) then it is termed as a non-linear differential equation.