87.14.10 problem 10

Internal problem ID [23529]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 109
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:42:44 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-7 x y^{\prime }+7 y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 34

ode:=(-x^2+1)*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+7*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x +\frac {c_2 \left (16 x^{6}-40 x^{4}+30 x^{2}-5\right )}{\left (x^{2}-1\right )^{{5}/{2}}} \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 86

ode=(1-x^2)*D[y[x],{x,2}]-7*x*D[y[x],x]+7*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 \sqrt {2} c_1 \left (-16 x^6+40 x^4-30 x^2+5\right )-\sqrt {\pi } c_2 \left (1-x^2\right )^{5/4} Q_{\frac {7}{2}}^{\frac {5}{2}}(x)}{\sqrt {\pi } \left (1-x^2\right )^{9/4} \sqrt [4]{x^2-1}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*x*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), (x, 2)) + 7*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False