64.6.4 problem 4

Internal problem ID [13283]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 4
Date solved : Monday, March 31, 2025 at 07:45:14 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \left (-\ln \left (x \right )+c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 16

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

\[ y(x)\to x^2 (-\log (x)+c_1) \]

✓ Sympy. Time used: 0.184 (sec). Leaf size: 10

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

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