32.6.31 problem Exercise 12.31, page 103

Internal problem ID [5896]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.31, page 103
Date solved : Tuesday, March 04, 2025 at 11:54:35 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 31

ode=x^2*D[y[x],x]+y[x]^2+x*y[x]+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: 0.228 (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)
 

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