49.22.5 problem 1(e)

Internal problem ID [7751]
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)
Date solved : Monday, January 27, 2025 at 03:12:02 PM
CAS classification : [_separable]

\begin{align*} x^{2} y^{3}-x^{3} y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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 &= 0 \\ y &= c_{1} x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 19

DSolve[x^2*y[x]^3-x^3*y[x]^2*D[y[x],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*}