85.33.28 problem 28

Internal problem ID [22651]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 28
Date solved : Thursday, October 02, 2025 at 09:02:44 PM
CAS classification : [_linear]

\begin{align*} x +2 y+x y^{\prime }&=0 \end{align*}

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

ode:=x+2*y(x)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x}{3}+\frac {c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 17

ode=(x+2*y[x])+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x}{3}+\frac {c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + x + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} - \frac {x}{3} \]