Internal problem ID [3250]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 506.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } y x -x -y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 31
dsolve(x*y(x)*diff(y(x),x) = x+y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {c_{1} x^{2}-2 x} \\ y \relax (x ) = -\sqrt {c_{1} x^{2}-2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.266 (sec). Leaf size: 42
DSolve[x y[x] y'[x]==x+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {-2+c_1 x} \\ y(x)\to \sqrt {x} \sqrt {-2+c_1 x} \\ \end{align*}