73.8.11 problem 13.2 (e)

Internal problem ID [15219]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.2 (e)
Date solved : Tuesday, January 28, 2025 at 07:50:15 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-{y^{\prime }}^{2}&=6 x^{5} \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 64

dsolve(x*diff(y(x),x$2)-diff(y(x),x)^2=6*x^5,y(x), singsol=all)
 

\[ y = \sqrt {6}\, \left (\int \frac {x^{{5}/{2}} \left (\operatorname {BesselY}\left (1, \frac {2 x^{{5}/{2}} \sqrt {6}}{5}\right ) c_{1} +\operatorname {BesselJ}\left (1, \frac {2 x^{{5}/{2}} \sqrt {6}}{5}\right )\right )}{c_{1} \operatorname {BesselY}\left (0, \frac {2 x^{{5}/{2}} \sqrt {6}}{5}\right )+\operatorname {BesselJ}\left (0, \frac {2 x^{{5}/{2}} \sqrt {6}}{5}\right )}d x \right )+c_{2} \]

✓ Solution by Mathematica

Time used: 60.325 (sec). Leaf size: 109

DSolve[x*D[y[x],{x,2}]-D[y[x],x]^2==6*x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\frac {\sqrt {6} \left (2 \operatorname {BesselY}\left (1,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right )+\operatorname {BesselJ}\left (1,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right ) c_1\right ) K[1]^{5/2}}{2 \operatorname {BesselY}\left (0,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right )+\operatorname {BesselJ}\left (0,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right ) c_1}dK[1]+c_2 \]