Internal problem ID [13607]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises.
page 641
Problem number: 33.5 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (-x^{2}+4\right ) y^{\prime \prime }-5 y^{\prime } x -3 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve((4-x^2)*diff(y(x),x$2)-5*x*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {3}{8} x^{2}+\frac {15}{128} x^{4}\right ) y \left (0\right )+\left (x +\frac {1}{3} x^{3}+\frac {1}{10} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[(4-x^2)*y''[x]-5*x*y'[x]-3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{10}+\frac {x^3}{3}+x\right )+c_1 \left (\frac {15 x^4}{128}+\frac {3 x^2}{8}+1\right ) \]