76.11.4 problem 4

Internal problem ID [17548]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.1 (Definitions and examples). Problems at page 214
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 10:43:15 AM
CAS classification : [_Bessel]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

\[ y = c_{1} \operatorname {BesselJ}\left (\nu , x\right )+c_{2} \operatorname {BesselY}\left (\nu , x\right ) \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 18

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

\[ y(x)\to c_1 \operatorname {BesselJ}(n,x)+c_2 \operatorname {BesselY}(n,x) \]