Internal problem ID [9391]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1812.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y \left (1-\ln \relax (y)\right ) y^{\prime \prime }+\left (1+\ln \relax (y)\right ) \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 19
dsolve(y(x)*(1-ln(y(x)))*diff(diff(y(x),x),x)+(1+ln(y(x)))*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x c_{1}+c_{2}-1}{x c_{1}+c_{2}}} \]
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 21
DSolve[(1 + Log[y[x]])*y'[x]^2 + (1 - Log[y[x]])*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{1-\frac {1}{c_1 (x+c_2)}} \\ \end{align*}