Internal problem ID [4159]
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.
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 }-y^{\prime } {\mathrm e}^{y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = 0, y^{\prime }\relax (3) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \relax (x ) = -\ln \left (4-x \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]==y'[x]*Exp[y[x]],{y[3]==0,y'[3]==1}},y[x],x,IncludeSingularSolutions -> True]
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