7.17.9 problem 9

Internal problem ID [522]
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 : 9
Date solved : Monday, January 27, 2025 at 02:54:23 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 25

dsolve(16*x^2*diff(y(x),x$2)-(5-144*x^3)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_1 \sin \left (2 x^{{3}/{2}}\right )+c_2 \cos \left (2 x^{{3}/{2}}\right )}{x^{{1}/{4}}} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 47

DSolve[16*x^2*D[y[x],{x,2}]-(5-144*x^3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-2 i x^{3/2}} \left (6 c_1 e^{4 i x^{3/2}}+i c_2\right )}{6 \sqrt [4]{x}} \]