Internal problem ID [10066]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1744 (book 6.153).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 77
dsolve(2*diff(diff(y(x),x),x)*y(x)-6*diff(y(x),x)^2+(1+a*y(x)^3)*y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ -2 \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{4} c_{1} +4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ 2 \left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{4} c_{1} +4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 47.786 (sec). Leaf size: 2761
DSolve[y[x]^2*(1 + a*y[x]^3) - 6*y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
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