64.3.17 problem 22

Internal problem ID [13217]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 22
Date solved : Monday, March 31, 2025 at 07:39:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

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

\[ y = \frac {x^{2}}{-x +c_1} \]

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 23

ode=(y[x]^2+2*x*y[x])-x^2*D[y[x],x]==0; 
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: 0.216 (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)
 

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