60.7.239 problem 1830 (book 6.239)

Internal problem ID [11828]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1830 (book 6.239)
Date solved : Tuesday, January 28, 2025 at 06:23:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} {y^{\prime \prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.958 (sec). Leaf size: 37

dsolve(3*x^2*diff(diff(y(x),x),x)^2-2*(3*x*diff(y(x),x)+y(x))*diff(diff(y(x),x),x)+4*diff(y(x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= x^{1+\frac {2 \sqrt {3}}{3}} c_{1} \\ y &= 0 \\ y &= \frac {c_{1}^{2} x^{2}}{c_{2}}+c_{1} x +c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

DSolve[4*D[y[x],x]^2 - 2*(y[x] + 3*x*D[y[x],x])*D[y[x],{x,2}] + 3*x^2*D[y[x],{x,2}]^2 == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1{}^2 x^2}{c_2}+c_1 x+c_2 \\ y(x)\to \text {Indeterminate} \\ \end{align*}