Internal problem ID [13916]
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: 33.3 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\frac {y}{x -1}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
Order:=6; dsolve(diff(y(x),x)+1/(x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (x^{5}+x^{4}+x^{3}+x^{2}+x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 21
AsymptoticDSolveValue[y'[x]+1/(x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (x^5+x^4+x^3+x^2+x+1\right ) \]