60.3.213 problem 1228

Internal problem ID [11209]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1228
Date solved : Sunday, March 30, 2025 at 07:46:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+a y&=0 \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 53

ode:=(x^2+1)*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+a*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 66

ode=a*y[x] + 3*x*D[y[x],x] + (1 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1 P_{\sqrt {1-a}-\frac {1}{2}}^{\frac {1}{2}}(i x)+c_2 Q_{\sqrt {1-a}-\frac {1}{2}}^{\frac {1}{2}}(i x)}{\sqrt [4]{x^2+1}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*y(x) + 3*x*Derivative(y(x), x) + (x**2 + 1)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False