Internal problem ID [12005]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number: 10.1 (ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y \,{\mathrm e}^{x}+y x \,{\mathrm e}^{x}+\left (x \,{\mathrm e}^{x}+2\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((1+exp(x)*y(x)+x*exp(x)*y(x))+(x*exp(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} -x}{{\mathrm e}^{x} x +2} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 21
DSolve[(1+Exp[x]*y[x]+x*Exp[x]*y[x])+(x*Exp[x]+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-x+c_1}{e^x x+2} \]