Internal problem ID [14779]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (x +2\right ) y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((x^2-4)*diff(y(x),x$2)+16*(x+2)*diff(y(x),x)-y(x)=0,y(x),type='series',x=1);
\[ y \left (x \right ) = \left (1-\frac {\left (-1+x \right )^{2}}{6}-\frac {25 \left (-1+x \right )^{3}}{27}-\frac {2699 \left (-1+x \right )^{4}}{648}-\frac {6404 \left (-1+x \right )^{5}}{405}\right ) y \left (1\right )+\left (-1+x +8 \left (-1+x \right )^{2}+\frac {815 \left (-1+x \right )^{3}}{18}+\frac {10991 \left (-1+x \right )^{4}}{54}+\frac {834547 \left (-1+x \right )^{5}}{1080}\right ) D\left (y \right )\left (1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 85
AsymptoticDSolveValue[(x^2-4)*y''[x]+16*(x+2)*y'[x]-y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (-\frac {6404}{405} (x-1)^5-\frac {2699}{648} (x-1)^4-\frac {25}{27} (x-1)^3-\frac {1}{6} (x-1)^2+1\right )+c_2 \left (\frac {834547 (x-1)^5}{1080}+\frac {10991}{54} (x-1)^4+\frac {815}{18} (x-1)^3+8 (x-1)^2+x-1\right ) \]