32.6.31 problem Exercise 12.31, page 103

Internal problem ID [5896]
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 12.31, page 103
Date solved : Monday, January 27, 2025 at 01:25:10 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \frac {x (\log (x)-1-c_1)}{-\log (x)+c_1} \\ y(x)\to -x \\ \end{align*}