32.10.17 problem Exercise 35.17, page 504

Internal problem ID [6011]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.17, page 504
Date solved : Monday, January 27, 2025 at 01:32:10 PM
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 (3\right )&=0\\ y^{\prime }\left (3\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)=diff(y(x),x)*exp(y(x)),y(3) = 0, D(y)(3) = 1],y(x), singsol=all)
 

\[ y = -\ln \left (-x +4\right ) \]

✓ Solution by Mathematica

Time used: 7.542 (sec). Leaf size: 13

DSolve[{D[y[x],{x,2}]==D[y[x],x]*Exp[y[x]],{y[3]==0,Derivative[1][y][3 ]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\log (4-x) \]