Internal problem ID [3005]
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]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+x^{2}+y x +y^{2}=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = -\frac {x \left (\ln \relax (x )+c_{1}-1\right )}{c_{1}+\ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 25
DSolve[x^2 y'[x]+x^2+x y[x]+y[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*}