23.3.122 problem 124

Internal problem ID [5836]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 124
Date solved : Friday, October 03, 2025 at 01:44:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 49

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

\[ y = c_1 \operatorname {KummerM}\left (\frac {c}{2 b}, \frac {1}{2}, -\frac {\left (b x +a \right )^{2}}{2 b}\right )+c_2 \operatorname {KummerU}\left (\frac {c}{2 b}, \frac {1}{2}, -\frac {\left (b x +a \right )^{2}}{2 b}\right ) \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 81

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

\begin{align*} y(x)&\to e^{-\frac {1}{2} x (2 a+b x)} \left (c_1 \operatorname {HermiteH}\left (\frac {c}{b}-1,\frac {a+b x}{\sqrt {2} \sqrt {b}}\right )+c_2 \operatorname {Hypergeometric1F1}\left (\frac {b-c}{2 b},\frac {1}{2},\frac {(a+b x)^2}{2 b}\right )\right ) \end{align*}

✗ Sympy

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

False