48.4.16 problem Problem 3.23

Internal problem ID [7558]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.23
Date solved : Thursday, March 13, 2025 at 06:03:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 99

ode:=(-x^2+1)*diff(diff(z(x),x),x)+(1-3*x)*diff(z(x),x)+k*z(x) = 0; 
dsolve(ode,z(x), singsol=all);
 

\[ z = c_{1} \left (x +1\right )^{-1-\sqrt {k +1}} \operatorname {hypergeom}\left (\left [\sqrt {k +1}, 1+\sqrt {k +1}\right ], \left [1+2 \sqrt {k +1}\right ], \frac {2}{x +1}\right )+c_{2} \left (x +1\right )^{-1+\sqrt {k +1}} \operatorname {hypergeom}\left (\left [-\sqrt {k +1}, 1-\sqrt {k +1}\right ], \left [1-2 \sqrt {k +1}\right ], \frac {2}{x +1}\right ) \]

✓ Mathematica. Time used: 0.279 (sec). Leaf size: 77

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

\[ z(x)\to c_2 G_{2,2}^{2,0}\left (\frac {1-x}{2}| \begin {array}{c} -\sqrt {k+1},\sqrt {k+1} \\ 0,0 \\ \end {array} \right )+c_1 \operatorname {Hypergeometric2F1}\left (1-\sqrt {k+1},\sqrt {k+1}+1,1,\frac {1-x}{2}\right ) \]

✗ Sympy

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

False