74.15.55 problem 54 (d)

Internal problem ID [16494]
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 : Tuesday, January 28, 2025 at 09:09:30 AM
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*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

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

\[ y = c_{1} \sin \left (2 \,\operatorname {arcsinh}\left (x \right )\right )+c_{2} \cos \left (2 \,\operatorname {arcsinh}\left (x \right )\right ) \]

✓ Solution by Mathematica

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

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

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