Internal problem ID [2073]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.8, page 68
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-y^{2}-3 y x -x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x)=y(x)^2+3*x*y(x)+x^2,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: 0.146 (sec). Leaf size: 25
DSolve[x^2*y'[x]==y[x]^2+3*x*y[x]+x^2,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*}