12.7.7 problem 7

Internal problem ID [1717]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:32:19 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve((x*y(x)+x+2*y(x)+1)+(x+1)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 23

DSolve[(x*y[x]+x+2*y[x]+1)+(x+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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