Internal problem ID [7720]
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]
\[ \boxed {x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(x^2*(diff(y(x),x)+y(x)^2) + a*x*y(x) + b=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {a -1+\tanh \left (\frac {\sqrt {a^{2}-2 a -4 b +1}\, \left (-\ln \left (x \right )+c_{1} \right )}{2}\right ) \sqrt {a^{2}-2 a -4 b +1}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.246 (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*}