Internal problem ID [7687]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 106.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }+x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(x*diff(y(x),x) + x^a*y(x)^2 + (a-b)*y(x)/2 + x^b=0,y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\frac {c_{1} a +c_{1} b +2 x^{\frac {a}{2}+\frac {b}{2}}}{a +b}\right ) x^{-\frac {a}{2}+\frac {b}{2}} \]
✓ Solution by Mathematica
Time used: 1.163 (sec). Leaf size: 40
DSolve[x*y'[x] + x^a*y[x]^2 + (a-b)*y[x]/2 + x^b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^{\frac {b-a}{2}} \tan \left (\frac {2 x^{\frac {a+b}{2}}}{a+b}-c_1\right ) \\ \end{align*}