74.15.55 problem 54 (d)

Internal problem ID [16423]
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 (d)
Date solved : Monday, March 31, 2025 at 02:52:58 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 (4 x^{2}-4\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = c_1 \sin \left (2 \,\operatorname {arcsinh}\left (x \right )\right )+c_2 \cos \left (2 \,\operatorname {arcsinh}\left (x \right )\right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 22

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

\[ y(x)\to c_1 \cos (2 \text {arcsinh}(x))+c_2 \sin (2 \text {arcsinh}(x)) \]

✗ Sympy

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

False