60.4.6 problem 1454

Internal problem ID [11429]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1454
Date solved : Thursday, March 13, 2025 at 08:53:07 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 55

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

\[ y = c_{1} \operatorname {AiryAi}\left (-\frac {2^{{2}/{3}} a^{{1}/{3}} x}{2}\right )^{2}+c_{2} \operatorname {AiryBi}\left (-\frac {2^{{2}/{3}} a^{{1}/{3}} x}{2}\right )^{2}+c_3 \operatorname {AiryAi}\left (-\frac {2^{{2}/{3}} a^{{1}/{3}} x}{2}\right ) \operatorname {AiryBi}\left (-\frac {2^{{2}/{3}} a^{{1}/{3}} x}{2}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 79

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

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

✗ Sympy

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

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