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 : Monday, January 27, 2025 at 03:11:30 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==(y[x]+x*Exp[-2*y[x]/x])/x,y[x],x,IncludeSingularSolutions -> True]
 

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