Internal problem ID [15219]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 361.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }-{\mathrm e}^{2 y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)=exp(2*y(x)),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y = -\frac {\ln \left (\left (x -1\right )^{2}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 13
DSolve[{y''[x]==Exp[2*y[x]],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\log (1-x) \]