32.6.11 problem Exercise 12.11, page 103

Internal problem ID [5876]
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 12.11, page 103
Date solved : Monday, January 27, 2025 at 01:22:53 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y \left (x \right ) = \frac {3 x^{2}}{3 c_{1} x^{3}-1} \]

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 26

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

\begin{align*} y(x)\to \frac {3 x^2}{-1+3 c_1 x^3} \\ y(x)\to 0 \\ \end{align*}