Internal problem ID [9247]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1668.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x -\left (1-y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.051 (sec). Leaf size: 24
dsolve(x*diff(diff(y(x),x),x)-(1-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 c_{1}+\tanh \left (\frac {\ln \relax (x )-c_{2}}{2 c_{1}}\right )}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 46
DSolve[(-1 + y[x])*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2-\sqrt {2} \sqrt {2+c_1} \tanh \left (\frac {\sqrt {2+c_1} (-\log (x)+2 c_2)}{\sqrt {2}}\right ) \\ \end{align*}