49.21.12 problem 4(d)

Internal problem ID [7742]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 4(d)
Date solved : Wednesday, March 05, 2025 at 04:53:51 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.432 (sec). Leaf size: 18

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

\[ y(x)\to \frac {1}{2} x \log (2 (\log (x)+c_1)) \]

✓ Sympy. Time used: 0.630 (sec). Leaf size: 14

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

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