7.17.4 problem 4

Internal problem ID [517]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 4
Date solved : Monday, January 27, 2025 at 02:54:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 55

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+(8+x)*y(x)=0,y(x), singsol=all)
 

\[ y = -\operatorname {BesselY}\left (0, 2 \sqrt {x}\right ) x^{3} c_2 +\operatorname {BesselY}\left (1, 2 \sqrt {x}\right ) x^{{5}/{2}} c_2 +x^{{5}/{2}} \operatorname {BesselJ}\left (1, 2 \sqrt {x}\right ) c_1 -x^{3} \operatorname {BesselJ}\left (0, 2 \sqrt {x}\right ) c_1 \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 36

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+(8+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x^3 \left (c_1 \operatorname {BesselJ}\left (2,2 \sqrt {x}\right )-c_2 \operatorname {BesselY}\left (2,2 \sqrt {x}\right )\right ) \]