Internal problem ID [7821]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 241.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x y y^{\prime }-y^{2}+a \,x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(2*x*y(x)*diff(y(x),x)-y(x)^2+a*x^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {-a \,x^{2}+c_{1} x} \\ y \relax (x ) = -\sqrt {-a \,x^{2}+c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.384 (sec). Leaf size: 37
DSolve[2*x*y[x]*y'[x]-y[x]^2+a*x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x (-a x+c_1)} \\ y(x)\to \sqrt {x (-a x+c_1)} \\ \end{align*}