Internal problem ID [10003]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1672 (book 6.81).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {2 y^{\prime \prime } x +{y^{\prime }}^{3}+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 35
dsolve(2*x*diff(diff(y(x),x),x)+diff(y(x),x)^3+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {2 \sqrt {x c_{1} -1}}{c_{1}}+c_{2} y \left (x \right ) = -\frac {2 \sqrt {x c_{1} -1}}{c_{1}}+c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.896 (sec). Leaf size: 65
DSolve[y'[x] + y'[x]^3 + 2*x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-2 i e^{c_1} \sqrt {-x+e^{2 c_1}} y(x)\to 2 i e^{c_1} \sqrt {-x+e^{2 c_1}}+c_2 y(x)\to c_2 \end{align*}