82.54.19 problem Ex. 19

Internal problem ID [19035]
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. 19
Date solved : Tuesday, January 28, 2025 at 12:46:17 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 25

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

\[ y(x)\to c_1 \cos \left (\frac {n}{x}\right )-c_2 \sin \left (\frac {n}{x}\right ) \]