38.6.24 problem 24

Internal problem ID [8454]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 24
Date solved : Tuesday, September 30, 2025 at 05:37:19 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=(x^2-1)*diff(y(x),x)+2*y(x) = (1+x)^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 68

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

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

✓ Sympy. Time used: 0.196 (sec). Leaf size: 15

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

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