44.6.12 problem 12

Internal problem ID [7156]
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, February 04, 2025 at 12:40:51 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 27

DSolve[(1+x)*D[y[x],x]-x*y[x]==x+x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^2+3 x-c_1 e^x+3}{x+1} \]