56.2.33 problem 32
Internal
problem
ID
[8837]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
2.0
Problem
number
:
32
Date
solved
:
Wednesday, March 05, 2025 at 06:52:50 AM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} y^{\prime \prime }-x y-x^{3}&=0 \end{align*}
✓ Maple. Time used: 0.008 (sec). Leaf size: 87
ode:=diff(diff(y(x),x),x)-x*y(x)-x^3 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {5 x^{4} \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right ) \pi \left (\operatorname {AiryBi}\left (x \right ) 3^{{1}/{3}}-\operatorname {AiryAi}\left (x \right ) 3^{{5}/{6}}\right )-6 \left (x^{5} \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \left (\operatorname {AiryAi}\left (x \right ) 3^{{2}/{3}}+\operatorname {AiryBi}\left (x \right ) 3^{{1}/{6}}\right ) \Gamma \left (\frac {2}{3}\right )-10 \operatorname {AiryBi}\left (x \right ) c_{1} -10 \operatorname {AiryAi}\left (x \right ) c_{2} \right ) \Gamma \left (\frac {2}{3}\right )}{60 \Gamma \left (\frac {2}{3}\right )}
\]
✓ Mathematica. Time used: 0.097 (sec). Leaf size: 137
ode=D[y[x],{x,2}]-x*y[x]-x^3==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to -\frac {\pi x^5 \operatorname {Gamma}\left (\frac {5}{3}\right ) \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {5}{3};\frac {4}{3},\frac {8}{3};\frac {x^3}{9}\right )}{9\ 3^{5/6} \operatorname {Gamma}\left (\frac {4}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right )}+\frac {\pi x^4 \operatorname {Gamma}\left (\frac {4}{3}\right ) \left (\operatorname {AiryBi}(x)-\sqrt {3} \operatorname {AiryAi}(x)\right ) \, _1F_2\left (\frac {4}{3};\frac {2}{3},\frac {7}{3};\frac {x^3}{9}\right )}{3\ 3^{2/3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {7}{3}\right )}+c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x)
\]
✓ Sympy. Time used: 0.058 (sec). Leaf size: 12
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x**3 - x*y(x) + Derivative(y(x), (x, 2)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} Ai\left (x\right ) + C_{2} Bi\left (x\right )
\]