23.5.21 problem 21

Internal problem ID [6630]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 21
Date solved : Friday, October 03, 2025 at 02:09:37 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 43

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

\[ y = c_1 \operatorname {AiryAi}\left (-\frac {2^{{2}/{3}} x}{2}\right )^{2}+c_2 \operatorname {AiryBi}\left (-\frac {2^{{2}/{3}} x}{2}\right )^{2}+c_3 \operatorname {AiryAi}\left (-\frac {2^{{2}/{3}} x}{2}\right ) \operatorname {AiryBi}\left (-\frac {2^{{2}/{3}} x}{2}\right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 59

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

\begin{align*} y(x)&\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-\frac {1}{2}} x\right )^2+c_3 \operatorname {AiryBi}\left (\sqrt [3]{-\frac {1}{2}} x\right )^2+c_2 \operatorname {AiryAi}\left (\sqrt [3]{-\frac {1}{2}} x\right ) \operatorname {AiryBi}\left (\sqrt [3]{-\frac {1}{2}} x\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-y(x) - Derivative(y(x), (x, 3)))/(2*x) c