Internal problem ID [3922]
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]
\[ \boxed {2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \sqrt {-\frac {2}{\operatorname {LambertW}\left (-2 c_{1} x^{4}\right )}}\, x \]
✓ Solution by Mathematica
Time used: 6.133 (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 {W\left (-2 e^{-2 c_1} x^4\right )}} \\ y(x)\to \frac {i \sqrt {2} x}{\sqrt {W\left (-2 e^{-2 c_1} x^4\right )}} \\ y(x)\to 0 \\ \end{align*}