32.6.26 problem Exercise 12.26, page 103

Internal problem ID [5891]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.26, page 103
Date solved : Monday, January 27, 2025 at 01:24:55 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^3*diff(y(x),x)-y(x)^2-x^2*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{2}}{c_{1} x +1} \]

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 22

DSolve[x^3*D[y[x],x]-y[x]^2-x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2}{1+c_1 x} \\ y(x)\to 0 \\ \end{align*}