56.2.29 problem 28
Internal
problem
ID
[8833]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
2.0
Problem
number
:
28
Date
solved
:
Sunday, March 30, 2025 at 01:41:09 PM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} y^{\prime \prime }-x y-x^{3}+2&=0 \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 18
ode:=diff(diff(y(x),x),x)-x*y(x)-x^3+2 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \operatorname {AiryAi}\left (x \right ) c_2 +\operatorname {AiryBi}\left (x \right ) c_1 -x^{2}
\]
✓ Mathematica. Time used: 0.428 (sec). Leaf size: 290
ode=D[y[x],{x,2}]-x*y[x]-x^3+2==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to \frac {6 \sqrt [3]{3} \pi x \operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {Gamma}\left (\frac {5}{3}\right ) \operatorname {Gamma}\left (\frac {7}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right ) \left (\sqrt {3} \operatorname {AiryAi}(x)-\operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {1}{3};\frac {2}{3},\frac {4}{3};\frac {x^3}{9}\right )+2 \sqrt [6]{3} \pi x^2 \operatorname {Gamma}\left (\frac {2}{3}\right )^2 \operatorname {Gamma}\left (\frac {7}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right ) \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {2}{3};\frac {4}{3},\frac {5}{3};\frac {x^3}{9}\right )+\operatorname {Gamma}\left (\frac {5}{3}\right ) \left (3 \sqrt [3]{3} \pi x^4 \operatorname {Gamma}\left (\frac {4}{3}\right )^2 \operatorname {Gamma}\left (\frac {8}{3}\right ) \left (\operatorname {AiryBi}(x)-\sqrt {3} \operatorname {AiryAi}(x)\right ) \, _1F_2\left (\frac {4}{3};\frac {2}{3},\frac {7}{3};\frac {x^3}{9}\right )+\operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {7}{3}\right ) \left (-\sqrt [6]{3} \pi x^5 \operatorname {Gamma}\left (\frac {5}{3}\right ) \left (3 \operatorname {AiryAi}(x)+\sqrt {3} \operatorname {AiryBi}(x)\right ) \, _1F_2\left (\frac {5}{3};\frac {4}{3},\frac {8}{3};\frac {x^3}{9}\right )+27 \operatorname {Gamma}\left (\frac {4}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right ) (c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x))\right )\right )}{27 \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {Gamma}\left (\frac {4}{3}\right ) \operatorname {Gamma}\left (\frac {5}{3}\right ) \operatorname {Gamma}\left (\frac {7}{3}\right ) \operatorname {Gamma}\left (\frac {8}{3}\right )}
\]
✓ Sympy. Time used: 0.065 (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)) + 2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} Ai\left (x\right ) + C_{2} Bi\left (x\right )
\]