89.3.5 problem 5

Internal problem ID [24303]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 34
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:12:44 PM
CAS classification : [_separable]

\begin{align*} 2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \frac {c_1 x}{\left (x +1\right )^{3}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {c_1 x}{(x+1)^3}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 19

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

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