Internal problem ID [5330]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
198
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} y^{3}-y^{2} y^{\prime } x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 11
dsolve(x^2*y(x)^3-x^3*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = c_{1} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 19
DSolve[x^2*y[x]^3-x^3*y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to c_1 x \\ y(x)\to 0 \\ \end{align*}