Euler's differential equation

 

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In mathematics, Euler's differential equation is a first order nonlinear ordinary differential equation, named after Leonhard Euler given by^[1]

${\displaystyle {\frac {dy}{dx}}+{\frac {\sqrt {a_{0}+a_{1}y+a_{2}y^{2}+a_{3}y^{3}+a_{4}y^{4}}}{\sqrt {a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}}}}=0}$

This is a separable equation and the solution is given by the following integral equation

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.