15.6.6 problem 6

Internal problem ID [2963]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:04:35 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

\[ x \left (y \right ) = \frac {{\mathrm e}^{y}+2 \,{\mathrm e}^{-y} c_{1}}{2 y} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 18

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

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