53.4.38 problem 41

Internal problem ID [8526]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 41
Date solved : Monday, January 27, 2025 at 04:09:19 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} {y^{\prime \prime }}^{3}&=12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.734 (sec). Leaf size: 173

dsolve(diff(y(x),x$2)^3=12*diff(y(x),x)*(x*diff(y(x),x$2)-2*diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {x^{4}}{9}+c_{1} \\ y &= c_{1} \\ y &= \int \operatorname {RootOf}\left (-6 \ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {3 \textit {\_f} \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, 2^{{1}/{3}} \left (\left (3 \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, \textit {\_f} +1\right )^{2} \left (9 \textit {\_f} -4\right )^{4}\right )^{{1}/{3}}-2 \,2^{{2}/{3}} \left (\left (3 \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, \textit {\_f} +1\right ) \left (9 \textit {\_f} -4\right )^{2}\right )^{{1}/{3}}-2^{{1}/{3}} \left (\left (3 \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, \textit {\_f} +1\right )^{2} \left (9 \textit {\_f} -4\right )^{4}\right )^{{1}/{3}}+18 \textit {\_f} -8}{\textit {\_f} \left (9 \textit {\_f} -4\right )}d \textit {\_f} +6 c_{1} \right ) x^{3}d x +c_{2} \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[(D[y[x],{x,2}])^3==12*D[y[x],x]*(x*D[y[x],{x,2}]-2*D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

Not solved