23.3.377 problem 381

Internal problem ID [6091]
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 : 381
Date solved : Tuesday, September 30, 2025 at 02:21:22 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} -\left (2-a \right ) y+a x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 36

ode:=-(2-a)*y(x)+a*x*diff(y(x),x)+(x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (x^{2}+1\right )^{1-\frac {a}{2}}+c_2 x \operatorname {hypergeom}\left (\left [1, -\frac {1}{2}+\frac {a}{2}\right ], \left [\frac {3}{2}\right ], -x^{2}\right ) \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 68

ode=-((2 - a)*y[x]) + a*x*D[y[x],x] + (1 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (x^2+1\right )^{\frac {1}{2}-\frac {a}{4}} \left (c_1 P_{\frac {a-4}{2}}^{\frac {a-2}{2}}(i x)+c_2 Q_{\frac {a-4}{2}}^{\frac {a-2}{2}}(i x)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*x*Derivative(y(x), x) + (a - 2)*y(x) + (x**2 + 1)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False