Internal problem ID [7743]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 163.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(2*x^2*diff(y(x),x) - 2*y(x)^2 - x*y(x) + 2*a^2*x=0,y(x), singsol=all)
\[ y \relax (x ) = -i \tan \left (\frac {2 i a -c_{1} \sqrt {x}}{\sqrt {x}}\right ) \sqrt {x}\, a \]
✓ Solution by Mathematica
Time used: 0.43 (sec). Leaf size: 43
DSolve[2*x^2*y'[x] - 2*y[x]^2 - x*y[x] + 2*a^2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-a^2} \sqrt {x} \tan \left (\frac {2 \sqrt {-a^2}}{\sqrt {x}}-c_1\right ) \\ \end{align*}