Internal problem ID [4044]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+y^{2}+x y+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x)+y(x)^2+x*y(x)+x^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (\ln \relax (x )+c_{1}-1\right )}{\ln \relax (x )+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 25
DSolve[x^2*y'[x]+y[x]^2+x*y[x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (-1+\frac {1}{\log (x)-c_1}\right ) \\ y(x)\to -x \\ \end{align*}