60.3.10 problem 1010

Internal problem ID [11006]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1010
Date solved : Sunday, March 30, 2025 at 07:38:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 42

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

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

✓ Sympy. Time used: 0.087 (sec). Leaf size: 42

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

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