56.2.40 problem 39
Internal
problem
ID
[8844]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
2.0
Problem
number
:
39
Date
solved
:
Monday, January 27, 2025 at 05:05:08 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
\begin{align*} y^{\prime \prime }-x^{3} y-x^{3}&=0 \end{align*}
✓ Solution by Maple
Time used: 0.010 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-x^3*y(x)-x^3=0,y(x), singsol=all)
\[
y = \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{5}, \frac {2 x^{{5}/{2}}}{5}\right ) c_{2} +\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{5}, \frac {2 x^{{5}/{2}}}{5}\right ) c_{1} -1
\]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 217
DSolve[D[y[x],{x,2}]-x^3*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to \frac {\sqrt [5]{-1} \operatorname {Gamma}\left (\frac {4}{5}\right ) \left (5^{4/5} x^5 \operatorname {Gamma}\left (\frac {6}{5}\right ) \operatorname {Hypergeometric0F1Regularized}\left (\frac {9}{5},\frac {x^5}{25}\right ) \operatorname {BesselI}\left (\frac {1}{5},\frac {2 x^{5/2}}{5}\right )+5\ 5^{2/5} \left (x^{5/2}\right )^{2/5} \operatorname {BesselI}\left (-\frac {1}{5},\frac {2 x^{5/2}}{5}\right )-5^{3/5} \left (x^{5/2}\right )^{6/5} \operatorname {Gamma}\left (\frac {1}{5}\right ) \operatorname {BesselI}\left (-\frac {4}{5},\frac {2 x^{5/2}}{5}\right ) \operatorname {BesselI}\left (-\frac {1}{5},\frac {2 x^{5/2}}{5}\right )\right )}{25 \sqrt [5]{x^{5/2}} \text {Root}\left [25 \text {$\#$1}^5+1\&,5\right ]}+\frac {c_1 \sqrt {x} \operatorname {Gamma}\left (\frac {4}{5}\right ) \operatorname {BesselI}\left (-\frac {1}{5},\frac {2 x^{5/2}}{5}\right )}{\sqrt [5]{5}}+\sqrt [5]{-\frac {1}{5}} c_2 \sqrt {x} \operatorname {Gamma}\left (\frac {6}{5}\right ) \operatorname {BesselI}\left (\frac {1}{5},\frac {2 x^{5/2}}{5}\right )
\]