23.3.198 problem 200

Internal problem ID [5912]
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 : 200
Date solved : Friday, October 03, 2025 at 01:45:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 66

ode:=(b2*x+b1)*y(x)+a*diff(y(x),x)+x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-i \sqrt {\operatorname {b2}}\, x} \left (\operatorname {KummerU}\left (\frac {a \sqrt {\operatorname {b2}}+i \operatorname {b1}}{2 \sqrt {\operatorname {b2}}}, a , 2 i \sqrt {\operatorname {b2}}\, x \right ) c_2 +\operatorname {KummerM}\left (\frac {a \sqrt {\operatorname {b2}}+i \operatorname {b1}}{2 \sqrt {\operatorname {b2}}}, a , 2 i \sqrt {\operatorname {b2}}\, x \right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 85

ode=(b1 + b2*x)*y[x] + a*D[y[x],x] + x*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-i \sqrt {\text {b2}} x} \left (c_1 \operatorname {HypergeometricU}\left (\frac {1}{2} \left (a+\frac {i \text {b1}}{\sqrt {\text {b2}}}\right ),a,2 i \sqrt {\text {b2}} x\right )+c_2 L_{-\frac {a}{2}-\frac {i \text {b1}}{2 \sqrt {\text {b2}}}}^{a-1}\left (2 i \sqrt {\text {b2}} x\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b1 = symbols("b1") 
b2 = symbols("b2") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), x) + x*Derivative(y(x), (x, 2)) + (b1 + b2*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None