Internal problem ID [9250]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1671.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } x +\left (y^{\prime }\right )^{3}+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.043 (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 \relax (x ) = \frac {2 \sqrt {x c_{1}-1}}{c_{1}}+c_{2} \\ y \relax (x ) = -\frac {2 \sqrt {x c_{1}-1}}{c_{1}}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.304 (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*}