69.1.23 problem 40

Internal problem ID [14097]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 40
Date solved : Wednesday, March 05, 2025 at 10:32:05 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 17

ode=(x+y[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: 0.170 (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)
 

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