72.3.8 problem 8

Internal problem ID [14601]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.4 page 61
Problem number : 8
Date solved : Monday, March 31, 2025 at 12:39:53 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{\frac {2}{y}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Maple. Time used: 0.209 (sec). Leaf size: 38

ode:=diff(y(t),t) = exp(2/y(t)); 
ic:=y(1) = 2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {2}{\operatorname {RootOf}\left (-2 \textit {\_Z} \,\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )-2 \textit {\_Z} \,{\mathrm e}^{-1}+2 \textit {\_Z} \,\operatorname {Ei}_{1}\left (1\right )-\textit {\_Z} t -2 \,{\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \right )} \]

✗ Mathematica

ode=D[y[t],t]==Exp[2/y[t]]; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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✓ Sympy. Time used: 0.791 (sec). Leaf size: 44

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(2/y(t)) + Derivative(y(t), t),0) 
ics = {y(1): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ - t + y{\left (t \right )} e^{- \frac {2}{y{\left (t \right )}}} + 2 \operatorname {Ei}{\left (\frac {2 e^{i \pi }}{y{\left (t \right )}} \right )} = \frac {- e + 2 + 2 e \operatorname {Ei}{\left (e^{i \pi } \right )}}{e} \]