Internal problem ID [7820]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 240.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x y^{\prime } y-y^{2}+x a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 33
dsolve(2*x*y(x)*diff(y(x),x)-y(x)^2+a*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-a x \ln \relax (x )+c_{1} x} \\ y \relax (x ) = -\sqrt {-a x \ln \relax (x )+c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.363 (sec). Leaf size: 39
DSolve[2*x*y[x]*y'[x]-y[x]^2+a*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x (-a \log (x)+c_1)} \\ y(x)\to \sqrt {x (-a \log (x)+c_1)} \\ \end{align*}