74.17.4 problem 4

Internal problem ID [16535]
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 : 4
Date solved : Tuesday, January 28, 2025 at 09:10:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

Order:=6; 
dsolve((x^2-25)^2*diff(y(x),x$2)-(x+5)*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{125} x^{2}-\frac {1}{46875} x^{3}-\frac {767}{7812500} x^{4}-\frac {4813}{7324218750} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{250} x^{2}-\frac {112}{46875} x^{3}+\frac {173}{3906250} x^{4}-\frac {409681}{7324218750} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 70

AsymptoticDSolveValue[(x^2-25)^2*D[y[x],{x,2}]-(x+5)*D[y[x],x]+10*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (-\frac {4813 x^5}{7324218750}-\frac {767 x^4}{7812500}-\frac {x^3}{46875}-\frac {x^2}{125}+1\right )+c_2 \left (-\frac {409681 x^5}{7324218750}+\frac {173 x^4}{3906250}-\frac {112 x^3}{46875}+\frac {x^2}{250}+x\right ) \]