12.7.2 problem 2(a)

Internal problem ID [1712]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 2(a)
Date solved : Tuesday, March 04, 2025 at 01:37:50 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

\[ y = \frac {x}{c_1 x +1} \]

✓ Mathematica. Time used: 0.107 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {x}{1-c_1 x} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 10

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

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