50.8.19 problem 4(c)

Internal problem ID [7935]
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)
Date solved : Sunday, March 30, 2025 at 12:38:37 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 24

ode:=y(x)*diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{c_1} \operatorname {Ei}_{1}\left (-\textit {\_Z} +c_1 \right )+x +c_2 \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.274 (sec). Leaf size: 80

ode=y[x]*D[y[x],{x,2}]+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve y(x)*Derivative(y(x), (x, 2)) + Derivative(y(x), x)