Internal problem ID [13632]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises.
page 678
Problem number: 34.5 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y=0} \] With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve((x^2-4)*diff(y(x),x$2)+(x^2+x-6)*y(x)=0,y(x),type='series',x=2);
\[ y \left (x \right ) = \left (1-\frac {5 \left (x -2\right )^{2}}{8}+\frac {\left (x -2\right )^{3}}{96}+\frac {49 \left (x -2\right )^{4}}{768}-\frac {37 \left (x -2\right )^{5}}{15360}\right ) y \left (2\right )+\left (x -2-\frac {5 \left (x -2\right )^{3}}{24}+\frac {\left (x -2\right )^{4}}{192}+\frac {47 \left (x -2\right )^{5}}{3840}\right ) D\left (y \right )\left (2\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 78
AsymptoticDSolveValue[(x^2-4)*y''[x]+(x^2+x-6)*y[x]==0,y[x],{x,2,5}]
\[ y(x)\to c_1 \left (-\frac {37 (x-2)^5}{15360}+\frac {49}{768} (x-2)^4+\frac {1}{96} (x-2)^3-\frac {5}{8} (x-2)^2+1\right )+c_2 \left (\frac {47 (x-2)^5}{3840}+\frac {1}{192} (x-2)^4-\frac {5}{24} (x-2)^3+x-2\right ) \]