Internal problem ID [3923]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number: First order with homogeneous Coefficients. Exercise 7.6, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {2 y x^{2}+y^{3}+\left (y^{2} x -2 x^{3}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 19
dsolve((2*x^2*y(x)+y(x)^3)+(x*y(x)^2-2*x^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {-\frac {2}{\LambertW \left (-2 c_{1} x^{4}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 18.239 (sec). Leaf size: 66
DSolve[(2*x^2*y[x]+y[x]^3)+(x*y[x]^2-2*x^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {2} x}{\sqrt {\text {ProductLog}\left (-2 e^{-2 c_1} x^4\right )}} \\ y(x)\to \frac {i \sqrt {2} x}{\sqrt {\text {ProductLog}\left (-2 e^{-2 c_1} x^4\right )}} \\ y(x)\to 0 \\ \end{align*}