Internal problem ID [11646]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x +y x +y=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+(x*y(x)+y(x)-1)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-x}+1}{x} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 19
DSolve[x*y'[x]+(x*y[x]+y[x]-1)==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1+c_1 e^{-x}}{x} \]