72.3.7 problem 7

Internal problem ID [14671]
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 : 7
Date solved : Tuesday, January 28, 2025 at 06:47:09 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.625 (sec). Leaf size: 37

dsolve([diff(y(t),t)=exp(2/y(t)),y(0) = 2],y(t), singsol=all)
 

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[t],t]==Exp[2/y[t]],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

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