87.6.22 problem 25

Internal problem ID [23339]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 53
Problem number : 25
Date solved : Thursday, October 02, 2025 at 09:38:47 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 12

ode:=x^2+y(x)^2-2*x*y(x)*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} y &= x \\ y &= \operatorname {csgn}\left (x \right ) x \\ \end{align*}

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 6

ode=(x^2+y[x]^2)-2*x*y[x]*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \end{align*}

✓ Sympy. Time used: 0.276 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 - 2*x*y(x)*Derivative(y(x), x) + y(x)**2,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x^{2}} \]