Internal problem ID [5493]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-{\mathrm e}^{y} y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 1.047 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)=diff(y(x),x)*exp(y(x)),y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = x +\ln \left (-\frac {1}{-2+{\mathrm e}^{x}}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]==y'[x]*Exp[y[x]],{y[0]==0,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
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