78.7.10 problem 2 (c)

Internal problem ID [18196]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 11 (Reduction of order). Problems at page 87
Problem number : 2 (c)
Date solved : Tuesday, January 28, 2025 at 11:37:46 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.246 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)=diff(y(x),x)*exp(y(x)),y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = x +\ln \left (-\frac {1}{-2+{\mathrm e}^{x}}\right ) \]

✗ Solution by Mathematica

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

DSolve[{D[y[x],{x,2}]==D[y[x],x]*Exp[y[x]],{y[0]==0,Derivative[1][y][0] == 2}},y[x],x,IncludeSingularSolutions -> True]
 

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