7.17.8 problem 8

Internal problem ID [521]
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 : 8
Date solved : Monday, January 27, 2025 at 02:54:23 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-12 x y^{\prime }+\left (15+16 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(4*x^2*diff(y(x),x$2)-12*x*diff(y(x),x)+(15+16*x)*y(x)=0,y(x), singsol=all)
 

\[ y = x^{2} \left (c_1 \operatorname {BesselJ}\left (1, 4 \sqrt {x}\right )+c_2 \operatorname {BesselY}\left (1, 4 \sqrt {x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 36

DSolve[4*x^2*D[y[x],{x,2}]-12*x*D[y[x],x]+(15+16*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 16 x^2 \left (c_1 \operatorname {BesselJ}\left (1,4 \sqrt {x}\right )+2 c_2 \operatorname {BesselY}\left (1,4 \sqrt {x}\right )\right ) \]