50.7.10 problem 2(c)

Internal problem ID [7914]
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. Section 1.9. Reduction of Order. Page 38
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 03:31:59 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \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: 0.436 (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)
 

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

✗ 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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