60.7.229 problem 1820 (book 6.229)

Internal problem ID [11818]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1820 (book 6.229)
Date solved : Tuesday, January 28, 2025 at 06:11:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.080 (sec). Leaf size: 46

dsolve(a*x^3*diff(y(x),x)*diff(diff(y(x),x),x)+y(x)^2*b=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\int _{}^{\ln \left (x \right )}\operatorname {RootOf}\left (-a \left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{\textit {\_a}^{3} a -a \,\textit {\_a}^{2}+b}d \textit {\_a} \right )-\textit {\_b} +c_{1} \right )d \textit {\_b} +c_{2}} \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[b*y[x]^2 + a*x^3*D[y[x],x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved