74.15.7 problem 7

Internal problem ID [16446]
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 : 7
Date solved : Tuesday, January 28, 2025 at 09:08:09 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(2*x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+20*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

DSolve[2*x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]