82.54.16 problem Ex. 16

Internal problem ID [19032]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 16
Date solved : Tuesday, January 28, 2025 at 12:46:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

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

\[ y \left (x \right ) = c_{1} \sin \left (n \sqrt {x^{2}-1}\right )+c_{2} \cos \left (n \sqrt {x^{2}-1}\right ) \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 36

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

\[ y(x)\to c_1 \cos \left (n \sqrt {x^2-1}\right )+c_2 \sin \left (n \sqrt {x^2-1}\right ) \]