6.8.6 problem 4

Internal problem ID [1742]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 05:18:54 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-5 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 17

ode:=(x^2-1)*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = 0; 
ic:=[y(0) = -5, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {-x +5}{x^{2}-1} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 18

ode=(x^2-1)*D[y[x],{x,2}]+4*x*D[y[x],x]+2*y[x]==0; 
ic={y[0]==-5,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5-x}{x^2-1} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x) + (x**2 - 1)*Derivative(y(x), (x, 2)) + 2*y(x),0) 
ics = {y(0): -5, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

False