Internal problem ID [7723]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 143.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }+a y^{2}\right )-b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 48
dsolve(x^2*(diff(y(x),x)+a*y(x)^2) - b=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {\tanh \left (-\frac {\ln \relax (x ) \sqrt {4 a b +1}}{2}+\frac {c_{1} \sqrt {4 a b +1}}{2}\right ) \sqrt {4 a b +1}-1}{2 a x} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 77
DSolve[x^2*(y'[x]+a*y[x]^2) - b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-1+\sqrt {4 a b+1} \left (-1+\frac {2 c_1}{x^{\sqrt {4 a b+1}}+c_1}\right )}{2 a x} \\ y(x)\to -\frac {\sqrt {4 a b+1}-1}{2 a x} \\ \end{align*}