74.18.54 problem 60

Internal problem ID [16611]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 60
Date solved : Tuesday, January 28, 2025 at 09:12:44 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y = x^{{3}/{5}} \left (c_{1} \sin \left (\frac {\ln \left (x \right )}{5}\right )+c_{2} \cos \left (\frac {\ln \left (x \right )}{5}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 32

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

\[ y(x)\to x^{3/5} \left (c_2 \cos \left (\frac {\log (x)}{5}\right )+c_1 \sin \left (\frac {\log (x)}{5}\right )\right ) \]