60.1.139 problem 140

Internal problem ID [10153]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 140
Date solved : Monday, January 27, 2025 at 06:30:14 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

dsolve(x^2*(diff(y(x),x)+y(x)^2) + 4*x*y(x) + 2=0,y(x), singsol=all)
 

\[ y = \frac {x -2 c_{1}}{\left (-x +c_{1} \right ) x} \]

✓ Solution by Mathematica

Time used: 0.164 (sec). Leaf size: 26

DSolve[x^2*(D[y[x],x]+y[x]^2) + 4*x*y[x] + 2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2}{x}+\frac {1}{x+c_1} \\ y(x)\to -\frac {2}{x} \\ \end{align*}