64.6.15 problem 15

Internal problem ID [13294]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 15
Date solved : Monday, March 31, 2025 at 07:47:05 AM
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 )&=2 \end{align*}

✓ Maple. Time used: 0.103 (sec). Leaf size: 11

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

\[ y = \sqrt {\left (x +3\right ) x} \]

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 18

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

\[ y(x)\to \sqrt {x} \sqrt {x+3} \]

✓ Sympy. Time used: 0.447 (sec). Leaf size: 10

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): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x \left (x + 3\right )} \]