7.7 problem 7

Internal problem ID [1067]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y x +x +2 y+1+\left (x +1\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 21

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

\[ y \relax (x ) = \frac {\left (-x \,{\mathrm e}^{x}+c_{1}\right ) {\mathrm e}^{-x}}{x +1} \]

Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {x-c_1 e^{-x}}{x+1} \\ \end{align*}