Internal problem ID [13975]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional
Exercises. page 715
Problem number: 35.2 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -1\right )^{2} y^{\prime \prime }-5 y^{\prime } \left (x -1\right )+9 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
Order:=6; dsolve((x-1)^2*diff(y(x),x$2)-5*(x-1)*diff(y(x),x)+9*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {9}{2} x^{2}+\frac {9}{2} x^{3}-\frac {3}{4} x^{4}-\frac {3}{20} x^{5}\right ) y \left (0\right )+\left (x -\frac {5}{2} x^{2}+\frac {11}{6} x^{3}-\frac {1}{4} x^{4}-\frac {1}{20} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 70
AsymptoticDSolveValue[(x-1)^2*y''[x]-5*(x-1)*y'[x]+9*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {3 x^5}{20}-\frac {3 x^4}{4}+\frac {9 x^3}{2}-\frac {9 x^2}{2}+1\right )+c_2 \left (-\frac {x^5}{20}-\frac {x^4}{4}+\frac {11 x^3}{6}-\frac {5 x^2}{2}+x\right ) \]