65.7.13 problem 17

Internal problem ID [15721]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:24:04 AM
CAS classification : [_separable]

\begin{align*} \left (2 x -1\right ) y+x \left (1+x \right ) y^{\prime }&=0 \end{align*}

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

ode:=y(x)*(2*x-1)+x*(1+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: 0.048 (sec). Leaf size: 38

ode=y[x]*(2*x-1)+x*(x+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \exp \left (\int _1^x\frac {1-2 K[1]}{K[1]^2+K[1]}dK[1]\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x + 1)*Derivative(y(x), x) + (2*x - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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