Internal problem ID [4161]
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 35.19, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }-{\mathrm e}^{y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 15
dsolve([2*diff(y(x),x$2)=exp(y(x)),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = 2 \ln \relax (2)+\ln \left (\frac {1}{\left (x -2\right )^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 15
DSolve[{2*y''[x]==Exp[y[x]],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \log \left (1-\frac {x}{2}\right ) \\ \end{align*}