Internal problem ID [6267]
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]]
\[ \boxed {y y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 24
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{c_{1}} \operatorname {Ei}_{1}\left (-\textit {\_Z} +c_{1} \right )+x +c_{2} \right )} \end{align*}
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 80
DSolve[y[x]*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [-e^{c_1} \operatorname {ExpIntegralEi}(\log (\text {$\#$1})-c_1)\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [-e^{-c_1} \operatorname {ExpIntegralEi}(\log (\text {$\#$1})--c_1)\&\right ][x+c_2] y(x)\to \text {InverseFunction}\left [-e^{c_1} \operatorname {ExpIntegralEi}(\log (\text {$\#$1})-c_1)\&\right ][x+c_2] \end{align*}