50.2.30 problem 29
Internal
problem
ID
[10120]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
2.0
Problem
number
:
29
Date
solved
:
Tuesday, September 30, 2025 at 07:03:17 PM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} y^{\prime \prime }-x y-x^{6}+64&=0 \end{align*}
✓ Maple. Time used: 0.008 (sec). Leaf size: 149
ode:=diff(diff(y(x),x),x)-x*y(x)-x^6+64 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {16 x^{7} \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{{1}/{3}}-3^{{5}/{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {7}{3}\right ], \left [\frac {2}{3}, \frac {10}{3}\right ], \frac {x^{3}}{9}\right )-21 x^{8} \Gamma \left (\frac {2}{3}\right )^{2} \left (3^{{1}/{6}} \operatorname {AiryBi}\left (x \right )+3^{{2}/{3}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {8}{3}\right ], \left [\frac {4}{3}, \frac {11}{3}\right ], \frac {x^{3}}{9}\right )-7168 x \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{{1}/{3}}-3^{{5}/{6}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{3}\right ], \left [\frac {2}{3}, \frac {4}{3}\right ], \frac {x^{3}}{9}\right )+5376 \left (x^{2} \Gamma \left (\frac {2}{3}\right ) \left (3^{{1}/{6}} \operatorname {AiryBi}\left (x \right )+3^{{2}/{3}} \operatorname {AiryAi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {2}{3}\right ], \left [\frac {4}{3}, \frac {5}{3}\right ], \frac {x^{3}}{9}\right )+\frac {\operatorname {AiryBi}\left (x \right ) c_1}{16}+\frac {\operatorname {AiryAi}\left (x \right ) c_2}{16}\right ) \Gamma \left (\frac {2}{3}\right )}{336 \Gamma \left (\frac {2}{3}\right )}
\]
✓ Mathematica. Time used: 0.098 (sec). Leaf size: 59
ode=D[y[x],{x,2}]-x*y[x]-x^6+64==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \operatorname {AiryAi}(x) \int _1^x-\pi \operatorname {AiryBi}(K[1]) \left (K[1]^6-64\right )dK[1]+\operatorname {AiryBi}(x) \int _1^x\pi \operatorname {AiryAi}(K[2]) \left (K[2]^6-64\right )dK[2]+c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x) \end{align*}
✓ Sympy. Time used: 0.038 (sec). Leaf size: 12
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x**6 - x*y(x) + Derivative(y(x), (x, 2)) + 64,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} Ai\left (x\right ) + C_{2} Bi\left (x\right )
\]