Internal problem ID [7721]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 141.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }+y^{2}\right )+a y x +b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 61
dsolve(x^2*(diff(y(x),x)+y(x)^2) + a*x*y(x) + b=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\tanh \left (-\frac {\ln \relax (x ) \sqrt {a^{2}-2 a -4 b +1}}{2}+\frac {c_{1} \sqrt {a^{2}-2 a -4 b +1}}{2}\right ) \sqrt {a^{2}-2 a -4 b +1}+a -1}{2 x} \]
✓ Solution by Mathematica
Time used: 0.389 (sec). Leaf size: 84
DSolve[x^2*(y'[x]+y[x]^2) + a*x*y[x] + b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {(a-1)^2-4 b} \left (1-\frac {2 c_1}{x^{\sqrt {(a-1)^2-4 b}}+c_1}\right )-a+1}{2 x} \\ y(x)\to -\frac {\sqrt {(a-1)^2-4 b}+a-1}{2 x} \\ \end{align*}