Internal problem ID [8434]
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]
\[ \boxed {y^{\prime } x +a y^{2}-y=-x^{2} b} \]
✓ 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)
\[ y \left (x \right ) = -\frac {\tan \left (c_{1} \sqrt {b a}+x \sqrt {b a}\right ) x \sqrt {b a}}{a} \]
✓ Solution by Mathematica
Time used: 16.893 (sec). Leaf size: 36
DSolve[x*y'[x] + a*y[x]^2 - y[x] + b*x^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} (x-c_1)\right )}{\sqrt {a}} \]