40.2.3 problem 26

Internal problem ID [6581]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 26
Date solved : Sunday, March 30, 2025 at 11:10:24 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (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: 0.131 (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: 0.162 (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)
 

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