Internal problem ID [7685]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 104.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }+a x y^{2}+2 y+b x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 63
dsolve(x*diff(y(x),x) + a*x*y(x)^2 + 2*y(x) + b*x=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {-\frac {i \sqrt {b}\, \sqrt {a}\, x -1}{x}+\frac {{\mathrm e}^{-2 i \sqrt {b}\, \sqrt {a}\, x}}{c_{1}-\frac {i {\mathrm e}^{-2 i \sqrt {b}\, \sqrt {a}\, x}}{2 \sqrt {b}\, \sqrt {a}}}}{a} \]
✓ Solution by Mathematica
Time used: 3.182 (sec). Leaf size: 43
DSolve[x*y'[x] + a*x*y[x]^2 + 2*y[x] + b*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{a x}-\sqrt {\frac {b}{a}} \tan \left (a x \sqrt {\frac {b}{a}}-c_1\right ) \\ \end{align*}