74.18.50 problem 56

Internal problem ID [16607]
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 : 56
Date solved : Tuesday, January 28, 2025 at 09:12:37 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{2}+c_{1}}{x^{4}} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^2+c_1}{x^4} \]