Internal problem ID [10130]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 13. Linear
equations of first order. Page 19
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x +\left (x +1\right ) y-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x*diff(y(x),x)+(1+x)*y(x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\frac {{\mathrm e}^{2 x}}{2}+c_{1}\right ) {\mathrm e}^{-x}}{x} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 25
DSolve[x*y'[x]+(1+x)*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x+2 c_1 e^{-x}}{2 x} \\ \end{align*}