74.17.26 problem 27 (b)

Internal problem ID [16557]
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 : 27 (b)
Date solved : Tuesday, January 28, 2025 at 09:10:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 35

Order:=6; 
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(16*x^2-25)*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{5} \left (1-\frac {2}{3} x^{2}+\frac {4}{21} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-1316818944000-1316818944000 x^{2}-877879296000 x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{5}} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 42

AsymptoticDSolveValue[x^2*D[y[x],{x,2}]+x*D[y[x],x]+(16*x^2-25)*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {1}{x^5}+\frac {1}{x^3}+\frac {2}{3 x}\right )+c_2 \left (\frac {4 x^9}{21}-\frac {2 x^7}{3}+x^5\right ) \]