60.1.137 problem 140

Internal problem ID [10151]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 140
Date solved : Sunday, March 30, 2025 at 03:20:12 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 20

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

\[ y = \frac {-2 c_1 +x}{x \left (-x +c_1 \right )} \]

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

ode=x^2*(D[y[x],x]+y[x]^2) + 4*x*y[x] + 2==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(y(x)**2 + Derivative(y(x), x)) + 4*x*y(x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- i \tan {\left (C_{1} + \frac {i \log {\left (x \right )}}{2} \right )} - 3}{2 x} \]