Internal problem ID [5514]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Problems for Review and Discovery. Page
53
Problem number: 4(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 24
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = {\mathrm e}^{\RootOf \left (-{\mathrm e}^{c_{1}} \expIntegral \left (1, -\textit {\_Z} +c_{1}\right )+x +c_{2}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 26
DSolve[y[x]*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [-e^{c_1} \text {ExpIntegralEi}(\log (\text {$\#$1})-c_1)\&\right ][x+c_2] \\ \end{align*}