35.8.11 problem 11

Internal problem ID [6218]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 11
Date solved : Wednesday, March 05, 2025 at 12:25:19 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

\[ y = \left (2 \ln \left (x \right )+c_{1} \right ) x \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 14

ode=(y[x]+2*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: 0.168 (sec). Leaf size: 10

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

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