64.6.10 problem 10

Internal problem ID [13360]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:31:58 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.113 (sec). Leaf size: 69

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

\[ y(x)\to \exp \left (\int _1^x-\frac {K[1]}{K[1]+1}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-K[2]-\int _1^{K[2]}-\frac {K[1]}{K[1]+1}dK[1]\right )}{K[2]+1}dK[2]+c_1\right ) \]