Internal problem ID [5459]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 1(j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{3}+y^{3}-x y^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 74
dsolve((x^3+y(x)^3)-(x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (3 \ln \relax (x )+c_{1}\right )^{\frac {1}{3}} x \\ y \relax (x ) = \left (-\frac {\left (3 \ln \relax (x )+c_{1}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (3 \ln \relax (x )+c_{1}\right )^{\frac {1}{3}}}{2}\right ) x \\ y \relax (x ) = \left (-\frac {\left (3 \ln \relax (x )+c_{1}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (3 \ln \relax (x )+c_{1}\right )^{\frac {1}{3}}}{2}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 63
DSolve[(x^3+y[x]^3)-(x*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sqrt [3]{3 \log (x)+c_1} \\ y(x)\to -\sqrt [3]{-1} x \sqrt [3]{3 \log (x)+c_1} \\ y(x)\to (-1)^{2/3} x \sqrt [3]{3 \log (x)+c_1} \\ \end{align*}