54.3.127 problem 1141

Internal problem ID [12422]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1141
Date solved : Wednesday, October 01, 2025 at 01:44:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 55

ode:=a*x*diff(diff(y(x),x),x)+(b*x+3*a)*diff(y(x),x)+3*b*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {Ei}_{1}\left (-\frac {x b}{a}\right ) {\mathrm e}^{-\frac {x b}{a}} c_2 \,b^{2} x^{2}+c_1 \,{\mathrm e}^{-\frac {x b}{a}} x^{2}+a c_2 \left (b x +a \right )}{x^{2}} \]

✓ Mathematica. Time used: 0.265 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to e^{-\frac {b x}{a}} \left (c_2 \int _1^x\frac {e^{\frac {b K[1]}{a}}}{K[1]^3}dK[1]+c_1\right ) \end{align*}

✗ Sympy

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

False