29.9.24 problem 264

Internal problem ID [4864]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 264
Date solved : Sunday, March 30, 2025 at 04:07:46 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 26

ode=x^2 D[y[x],x]+2 + x y[x](4+x y[x])==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: 0.224 (sec). Leaf size: 20

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

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