54.3.72 problem 1086

Internal problem ID [12367]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1086
Date solved : Wednesday, October 01, 2025 at 01:43:58 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 y^{\prime \prime }+9 x y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=4*diff(diff(y(x),x),x)+9*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {AiryAi}\left (-\frac {3^{{2}/{3}} 2^{{1}/{3}} x}{2}\right )+c_2 \operatorname {AiryBi}\left (-\frac {3^{{2}/{3}} 2^{{1}/{3}} x}{2}\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 48

ode=9*x*y[x] + 4*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.042 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x*y(x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} Ai\left (- \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} x}{2}\right ) + C_{2} Bi\left (- \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} x}{2}\right ) \]