Internal problem ID [14827]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +\left (16 x^{2}-25\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (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);
\[ y \left (x \right ) = c_{1} x^{5} \left (1-\frac {2}{3} x^{2}+\frac {4}{21} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-1316818944000-1316818944000 x^{2}-877879296000 x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{5}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 42
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]+(16*x^2-25)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^5}+\frac {1}{x^3}+\frac {2}{3 x}\right )+c_2 \left (\frac {4 x^9}{21}-\frac {2 x^7}{3}+x^5\right ) \]