60.7.163 problem 1754 (book 6.163)

Internal problem ID [11752]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1754 (book 6.163)
Date solved : Monday, January 27, 2025 at 11:34:05 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 12 y^{\prime \prime } y-15 {y^{\prime }}^{2}+8 y^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.074 (sec). Leaf size: 151

dsolve(12*diff(diff(y(x),x),x)*y(x)-15*diff(y(x),x)^2+8*y(x)^3=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ -\frac {12 y \left (8 \sqrt {y}-c_{1} \right ) \sqrt {8 y-c_{1} \sqrt {y}}}{\sqrt {-24 y^{3}+3 c_{1} y^{{5}/{2}}}\, c_{1} \sqrt {\sqrt {y}\, \left (8 \sqrt {y}-c_{1} \right )}}-x -c_{2} &= 0 \\ \frac {12 y \left (8 \sqrt {y}-c_{1} \right ) \sqrt {8 y-c_{1} \sqrt {y}}}{\sqrt {-24 y^{3}+3 c_{1} y^{{5}/{2}}}\, c_{1} \sqrt {\sqrt {y}\, \left (8 \sqrt {y}-c_{1} \right )}}-x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.695 (sec). Leaf size: 48

DSolve[8*y[x]^3 - 15*D[y[x],x]^2 + 12*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2304 c_1{}^2}{\left (3 c_1{}^2 x^2+6 c_2 c_1{}^2 x+128+3 c_2{}^2 c_1{}^2\right ){}^2} \\ y(x)\to 0 \\ \end{align*}