38.6.12 problem 12

Internal problem ID [8442]
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 : 12
Date solved : Tuesday, September 30, 2025 at 05:36:53 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \frac {c_1 \,{\mathrm e}^{x}-x^{2}-3 x -3}{1+x} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 58

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

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

✓ Sympy. Time used: 0.177 (sec). Leaf size: 19

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

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