Internal problem ID [3012]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 264.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2+x y \left (4+y x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x)+2+x*y(x)*(4+x*y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 c_{1}-x}{x \left (-x +c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 26
DSolve[x^2 y'[x]+2 + x y[x](4+x y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{x}+\frac {1}{x+c_1} \\ y(x)\to -\frac {2}{x} \\ \end{align*}