Internal problem ID [4667]
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]]
\[ \boxed {y^{\prime \prime }-y^{\prime } {\mathrm e}^{y}=0} \] With initial conditions \begin {align*} [y \left (3\right ) = 0, y^{\prime }\left (3\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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)
\[ y \left (x \right ) = -\ln \left (-x +4\right ) \]
✓ Solution by Mathematica
Time used: 7.673 (sec). Leaf size: 13
DSolve[{y''[x]==y'[x]*Exp[y[x]],{y[3]==0,y'[3]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\log (4-x) \]