Internal problem ID [15204]
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: 346.
ODE order: 2.
ODE degree: 0.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime } \ln \left (y^{\prime }\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)=diff(y(x),x)*ln(diff(y(x),x)),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y = -\operatorname {expIntegral}_{1}\left (-2 i \pi \_Z5 \,{\mathrm e}^{x}\right )+\operatorname {expIntegral}_{1}\left (-2 i \pi \_Z5 \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]==y'[x]*Log[y'[x]],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
{}