56.2.32 problem 31

Internal problem ID [8836]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 31
Date solved : Sunday, March 30, 2025 at 01:41:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-x y-x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)-x*y(x)-x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {AiryAi}\left (x \right ) c_2 +\operatorname {AiryBi}\left (x \right ) c_1 -x \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 30

ode=D[y[x],{x,2}]-x*y[x]-x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \pi x \operatorname {AiryAiPrime}(x) \operatorname {AiryBi}(x)+c_2 \operatorname {AiryBi}(x)+\operatorname {AiryAi}(x) (-\pi x \operatorname {AiryBiPrime}(x)+c_1) \]

✓ Sympy. Time used: 0.057 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - x*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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