Internal problem ID [10035]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1704 (book 6.113).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} \ln \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2-y(x)^2*ln(y(x))=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {{\mathrm e}^{-2 x} c_{1} {\mathrm e}^{x}}{2}} {\mathrm e}^{-\frac {c_{2} {\mathrm e}^{x}}{2}} \]
✓ Solution by Mathematica
Time used: 4.551 (sec). Leaf size: 73
DSolve[-(Log[y[x]]*y[x]^2) - y'[x]^2 + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-\frac {1}{2} \sqrt {c_1} e^{-x-c_2} \left (-1+e^{2 (x+c_2)}\right )\right ) y(x)\to \exp \left (\frac {1}{2} \sqrt {c_1} e^{-x-c_2} \left (-1+e^{2 (x+c_2)}\right )\right ) \end{align*}