Internal problem ID [7678]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }+a y^{2}-y+x^{2} b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(x*diff(y(x),x) + a*y(x)^2 - y(x) + b*x^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\tan \left (c_{1} \sqrt {a b}+x \sqrt {a b}\right ) x \sqrt {a b}}{a} \]
✓ Solution by Mathematica
Time used: 22.381 (sec). Leaf size: 36
DSolve[x*y'[x] + a*y[x]^2 - y[x] + b*x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} (x-c_1)\right )}{\sqrt {a}} \\ \end{align*}