74.15.6 problem 6

Internal problem ID [16445]
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 : 6
Date solved : Tuesday, January 28, 2025 at 09:08:06 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(9*x^2*diff(y(x),x$2)-9*x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} \sin \left (\frac {\ln \left (x \right )}{3}\right )+c_{2} \cos \left (\frac {\ln \left (x \right )}{3}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 28

DSolve[9*x^2*D[y[x],{x,2}]-9*x*D[y[x],x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_2 \cos \left (\frac {\log (x)}{3}\right )+c_1 \sin \left (\frac {\log (x)}{3}\right )\right ) \]