50.2.33 problem 32

Internal problem ID [10123]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 32
Date solved : Tuesday, September 30, 2025 at 07:03:23 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-x y-x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.062 (sec). Leaf size: 87

ode:=diff(diff(y(x),x),x)-x*y(x)-x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 \pi \left (-3^{{5}/{6}} \operatorname {AiryAi}\left (x \right )+3^{{1}/{3}} \operatorname {AiryBi}\left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {4}{3}\right ], \left [\frac {2}{3}, \frac {7}{3}\right ], \frac {x^{3}}{9}\right ) x^{4}-6 \left (x^{5} \operatorname {hypergeom}\left (\left [\frac {5}{3}\right ], \left [\frac {4}{3}, \frac {8}{3}\right ], \frac {x^{3}}{9}\right ) \left (3^{{2}/{3}} \operatorname {AiryAi}\left (x \right )+3^{{1}/{6}} \operatorname {AiryBi}\left (x \right )\right ) \Gamma \left (\frac {2}{3}\right )-10 \operatorname {AiryBi}\left (x \right ) c_1 -10 \operatorname {AiryAi}\left (x \right ) c_2 \right ) \Gamma \left (\frac {2}{3}\right )}{60 \Gamma \left (\frac {2}{3}\right )} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 55

ode=D[y[x],{x,2}]-x*y[x]-x^3==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]) K[1]^3dK[1]+\operatorname {AiryBi}(x) \int _1^x\pi \operatorname {AiryAi}(K[2]) K[2]^3dK[2]+c_1 \operatorname {AiryAi}(x)+c_2 \operatorname {AiryBi}(x) \end{align*}

✓ Sympy. Time used: 0.034 (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)
 

\[ y{\left (x \right )} = C_{1} Ai\left (x\right ) + C_{2} Bi\left (x\right ) \]