15.2.2 problem 2

Internal problem ID [2872]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 2
Date solved : Sunday, March 30, 2025 at 12:35:46 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +y\right ) y^{\prime }+x&=y \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 24

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

\[ y = \tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_1 \right )\right ) x \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 1.373 (sec). Leaf size: 26

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

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