60.7.153 problem 1744 (book 6.153)

Internal problem ID [11742]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1744 (book 6.153)
Date solved : Monday, January 27, 2025 at 11:32:18 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.079 (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 &= 0 \\ -2 \left (\int _{}^{y}\frac {1}{\sqrt {4 c_{1} \textit {\_a}^{4}+4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ 2 \left (\int _{}^{y}\frac {1}{\sqrt {4 c_{1} \textit {\_a}^{4}+4 \textit {\_a}^{3} a +1}\, \textit {\_a}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 37.208 (sec). Leaf size: 2761

DSolve[y[x]^2*(1 + a*y[x]^3) - 6*D[y[x],x]^2 + 2*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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