60.1.140 problem 141

Internal problem ID [10154]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 141
Date solved : Monday, January 27, 2025 at 06:30:16 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 50

dsolve(x^2*(diff(y(x),x)+y(x)^2) + a*x*y(x) + b=0,y(x), singsol=all)
 

\[ y = \frac {1-a +\tanh \left (\frac {\sqrt {a^{2}-2 a -4 b +1}\, \left (\ln \left (x \right )-c_{1} \right )}{2}\right ) \sqrt {a^{2}-2 a -4 b +1}}{2 x} \]

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 90

DSolve[x^2*(D[y[x],x]+y[x]^2) + a*x*y[x] + b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt {a^2-2 a-4 b+1} \left (1-\frac {2 c_1}{x^{\sqrt {a^2-2 a-4 b+1}}+c_1}\right )-a+1}{2 x} \\ y(x)\to -\frac {\sqrt {a^2-2 a-4 b+1}+a-1}{2 x} \\ \end{align*}