74.17.15 problem 15

Internal problem ID [16546]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 09:10:34 AM
CAS classification : [[_Emden, _Fowler]]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 25

Order:=6; 
dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)-7*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x \left (1+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-203212800+\operatorname {O}\left (x^{6}\right )\right )}{x^{7}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 14

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]+7*x*D[y[x],x]-7*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {c_1}{x^7}+c_2 x \]