Internal problem ID [3513]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 257.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{2}+y x +y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x)+x^2+x*y(x)+y(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: 0.144 (sec). Leaf size: 31
DSolve[x^2 y'[x]+x^2+x y[x]+y[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*}