ABSTRACT

If, in a differential equation, either the independent or the dependent variable does not appear it is possible to reduce the order of the equation. For example, the variable y is not explicitly present in the equation d 2 y d x 2 + 3 x 2 dy dx = 0 . $$ \frac{{d^{2} y}}{{dx^{2} }} + 3x^{2} \frac{{dy}}{{dx}} = 0 . $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108858/f4dff3a2-1feb-457b-a709-022257f02721/content/math5_1.tif"/>