Internal problem ID [14816]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (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);
\[ y \left (x \right ) = c_{1} x \left (1+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-203212800+\operatorname {O}\left (x^{6}\right )\right )}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 14
AsymptoticDSolveValue[x^2*y''[x]+7*x*y'[x]-7*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_1}{x^7}+c_2 x \]