80.3.5 problem 5

Internal problem ID [18478]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 5
Date solved : Monday, March 31, 2025 at 05:36:01 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y y^{\prime }&=m y \end{align*}

✓ Maple. Time used: 0.062 (sec). Leaf size: 57

ode:=x+y(x)*diff(y(x),x) = m*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{\operatorname {RootOf}\left (x^{2} \left (4 \,{\mathrm e}^{\textit {\_Z}} {\cosh \left (\frac {\sqrt {m^{2}-4}\, \left (2 c_1 +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 m}\right )}^{2}+m^{2}-4\right )\right )}+1-\textit {\_Z} m \right ) x \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 72

ode=x+y[x]*D[y[x],x]==m*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {m \arctan \left (\frac {\frac {2 y(x)}{x}-m}{\sqrt {4-m^2}}\right )}{\sqrt {4-m^2}}+\frac {1}{2} \log \left (-\frac {m y(x)}{x}+\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded