Internal problem ID [9266]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1687.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 23
dsolve(x^4*diff(diff(y(x),x),x)-x*(x^2+2*y(x))*diff(y(x),x)+4*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (-\ln \relax (x ) c_{1}+c_{2} c_{1}\right ) x^{2} c_{1}+x^{2} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 62
DSolve[4*y[x]^2 - x*(x^2 + 2*y[x])*y'[x] + x^4*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (\frac {2 i \sqrt {-1-c_1} c_2}{x^{2 i \sqrt {-1-c_1}}+c_2}+1-i \sqrt {-1-c_1}\right ) \\ \end{align*}