Internal problem ID [10089]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1767 (book 6.176).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {x y y^{\prime \prime }-4 x {y^{\prime }}^{2}+4 y^{\prime } y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 68
dsolve(x*y(x)*diff(diff(y(x),x),x)-4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {x}{\left (-3 c_{2} x^{3}+c_{1} \right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) x}{2 \left (-3 c_{2} x^{3}+c_{1} \right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) x}{2 \left (-3 c_{2} x^{3}+c_{1} \right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.67 (sec). Leaf size: 26
DSolve[4*y[x]*y'[x] - 4*x*y'[x]^2 + x*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x}{\sqrt [3]{1+c_1 x^3}} \\ y(x)\to 0 \\ \end{align*}