Internal problem ID [8576]
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]
\[ \boxed {2 x y^{\prime } y-y^{2}=-x a} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(2*x*y(x)*diff(y(x),x)-y(x)^2+a*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {-x \left (a \ln \left (x \right )-c_{1} \right )} \\ y \left (x \right ) &= -\sqrt {-x \left (a \ln \left (x \right )-c_{1} \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.413 (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*}