74.15.5 problem 5

Internal problem ID [16444]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 09:08:05 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+17 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(4*x^2*diff(y(x),x$2)+17*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, \left (c_{1} \sin \left (2 \ln \left (x \right )\right )+c_{2} \cos \left (2 \ln \left (x \right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 28

DSolve[4*x^2*D[y[x],{x,2}]+17*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} (c_2 \cos (2 \log (x))+c_1 \sin (2 \log (x))) \]