29.9.17 problem 257

Internal problem ID [4857]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 257
Date solved : Sunday, March 30, 2025 at 04:04:29 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }+x^{2}+x y+y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

\[ y = -\frac {x \left (\ln \left (x \right )+c_1 -1\right )}{\ln \left (x \right )+c_1} \]

✓ Mathematica. Time used: 0.158 (sec). Leaf size: 31

ode=x^2 D[y[x],x]+x^2+x y[x]+y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.217 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = x \left (8 x^{2} - 1\right ) \]