Internal problem ID [13483]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-{y^{\prime }}^{2}=6 x^{5}} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 64
dsolve(x*diff(y(x),x$2)-diff(y(x),x)^2=6*x^5,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {6}\, \left (\int \frac {x^{\frac {5}{2}} \left (\operatorname {BesselY}\left (1, \frac {2 x^{\frac {5}{2}} \sqrt {6}}{5}\right ) c_{1} +\operatorname {BesselJ}\left (1, \frac {2 x^{\frac {5}{2}} \sqrt {6}}{5}\right )\right )}{c_{1} \operatorname {BesselY}\left (0, \frac {2 x^{\frac {5}{2}} \sqrt {6}}{5}\right )+\operatorname {BesselJ}\left (0, \frac {2 x^{\frac {5}{2}} \sqrt {6}}{5}\right )}d x \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 60.384 (sec). Leaf size: 109
DSolve[x*y''[x]-y'[x]^2==6*x^5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \int _1^x\frac {\sqrt {6} \left (2 \operatorname {BesselY}\left (1,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right )+\operatorname {BesselJ}\left (1,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right ) c_1\right ) K[1]^{5/2}}{2 \operatorname {BesselY}\left (0,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right )+\operatorname {BesselJ}\left (0,\frac {2}{5} \sqrt {6} K[1]^{5/2}\right ) c_1}dK[1]+c_2 \]