62.1.4 problem Ex 4

Internal problem ID [12722]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 8. Exact differential equations. Page 11
Problem number : Ex 4
Date solved : Wednesday, March 05, 2025 at 08:19:36 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = -\frac {x}{2}+\frac {c_{1}}{x} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 17

ode=(y[x]+x)+ x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.173 (sec). Leaf size: 8

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

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