78.8.48 problem 48

Internal problem ID [18167]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 48
Date solved : Thursday, March 13, 2025 at 11:47:56 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {x^{2}}{-x +c_{1}} \]

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {x^2}{x-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 8

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

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