60.7.113 problem 1704 (book 6.113)

Internal problem ID [11702]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1704 (book 6.113)
Date solved : Monday, January 27, 2025 at 11:30:20 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} \ln \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 18

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)
 

\[ y = {\mathrm e}^{\frac {c_{1} {\mathrm e}^{-x}}{2}-\frac {{\mathrm e}^{x} c_{2}}{2}} \]

✓ Solution by Mathematica

Time used: 1.007 (sec). Leaf size: 63

DSolve[-(Log[y[x]]*y[x]^2) - D[y[x],x]^2 + y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{\frac {1}{2} \left (e^{x+c_2}-c_1 e^{-x-c_2}\right )} \\ y(x)\to e^{\frac {1}{2} \left (e^{-x-c_2}-c_1 e^{x+c_2}\right )} \\ \end{align*}