Internal problem ID [6105]
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.
ODE order: 2.
ODE degree: 3.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (y^{\prime \prime }\right )^{3}-12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.921 (sec). Leaf size: 174
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 \relax (x ) = \frac {x^{4}}{9}+c_{1} \\ y \relax (x ) = c_{1} \\ y \relax (x ) = \int \RootOf \left (-6 \ln \relax (x )-\left (\int _{}^{\textit {\_Z}}\frac {3 \textit {\_f} \sqrt {\frac {1}{\textit {\_f} \left (9 \textit {\_f} -4\right )}}\, 2^{\frac {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 )^{\frac {1}{3}}-2 \,2^{\frac {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 )^{\frac {1}{3}}-2^{\frac {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 )^{\frac {1}{3}}+18 \textit {\_f} -8}{\textit {\_f} \left (9 \textit {\_f} -4\right )}d \textit {\_f} \right )+6 c_{1}\right ) x^{3}d x +c_{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y''[x])^3==12*y'[x]*(x*y''[x]-2*y'[x]),y[x],x,IncludeSingularSolutions -> True]
Not solved