Internal problem ID [9289]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1715 (book 6.124).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime } y-3 {y^{\prime }}^{2}+3 y^{\prime } y-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 71
dsolve(diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+3*y(x)*diff(y(x),x)-y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 \\ y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {\left (c_{1} {\mathrm e}^{x}-c_{2} \right ) {\mathrm e}^{2 x}}}{2 \left (c_{1} {\mathrm e}^{x}-c_{2} \right )} \\ y \left (x \right ) = \frac {\sqrt {2}\, \sqrt {\left (c_{1} {\mathrm e}^{x}-c_{2} \right ) {\mathrm e}^{2 x}}}{2 c_{1} {\mathrm e}^{x}-2 c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.122 (sec). Leaf size: 28
DSolve[-y[x]^2 + 3*y[x]*y'[x] - 3*y'[x]^2 + y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 e^{x+c_1}}{\sqrt {-1+2 e^{x+c_1}}} \\ \end{align*}