74.15.56 problem 54 (e)

Internal problem ID [16424]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 54 (e)
Date solved : Monday, March 31, 2025 at 02:53:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 9

ode:=(x^4-1)*diff(diff(y(x),x),x)+(x^3-x)*diff(y(x),x)+(x^2-1)*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\sin \left (\operatorname {arcsinh}\left (x \right )\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 10

ode=(x^4-1)*D[y[x],{x,2}]+(x^3-x)*D[y[x],x]+(x^2-1)*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\sin (\text {arcsinh}(x)) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 - 1)*y(x) + (x**3 - x)*Derivative(y(x), x) + (x**4 - 1)*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

False