Internal problem ID [1992]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y x^{\prime }+\left (y +1\right ) x={\mathrm e}^{y}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(y*diff(x(y),y)+(1+y)*x(y)=exp(y),x(y), singsol=all)
\[ x \left (y \right ) = \frac {\left (\frac {{\mathrm e}^{2 y}}{2}+c_{1} \right ) {\mathrm e}^{-y}}{y} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 18
DSolve[y*x'[y]+(1+y)*x[y]==Exp[-y],x[y],y,IncludeSingularSolutions -> True]
\[ x(y)\to \frac {e^{-y} (y+c_1)}{y} \]