56.2.26 problem 25

Internal problem ID [8830]
Book : Own collection of miscellaneous problems
Section : section 2.0
Problem number : 25
Date solved : Sunday, March 30, 2025 at 01:41:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)-8*diff(y(x),x)-x*y(x)-x^3+2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{4 x} \operatorname {AiryAi}\left (16+x \right ) c_2 +{\mathrm e}^{4 x} \operatorname {AiryBi}\left (16+x \right ) c_1 -x^{2}+16 \]

✓ Mathematica. Time used: 6.257 (sec). Leaf size: 89

ode=D[y[x],{x,2}]-8*D[y[x],x]-x*y[x]-x^3+2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{4 x} \left (\operatorname {AiryAi}(x+16) \int _1^x-e^{-4 K[1]} \pi \operatorname {AiryBi}(K[1]+16) \left (K[1]^3-2\right )dK[1]+\operatorname {AiryBi}(x+16) \int _1^xe^{-4 K[2]} \pi \operatorname {AiryAi}(K[2]+16) \left (K[2]^3-2\right )dK[2]+c_1 \operatorname {AiryAi}(x+16)+c_2 \operatorname {AiryBi}(x+16)\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 - x*y(x) - 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE x**3/8 + x*y(x)/8 + Derivative(y(x), x) - Derivative(y(x), (x, 2))/8 - 1/4 cannot be solved by the factorable group method