Internal problem ID [13917]
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 (g).
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 \(x = 3\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
Order:=6; dsolve(diff(y(x),x)+1/(x-1)*y(x)=0,y(x),type='series',x=3);
\[ y \left (x \right ) = \left (\frac {5}{2}-\frac {x}{2}+\frac {\left (-3+x \right )^{2}}{4}-\frac {\left (-3+x \right )^{3}}{8}+\frac {\left (-3+x \right )^{4}}{16}-\frac {\left (-3+x \right )^{5}}{32}\right ) y \left (3\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 53
AsymptoticDSolveValue[y'[x]+1/(x-1)*y[x]==0,y[x],{x,3,5}]
\[ y(x)\to c_1 \left (-\frac {1}{32} (x-3)^5+\frac {1}{16} (x-3)^4-\frac {1}{8} (x-3)^3+\frac {1}{4} (x-3)^2+\frac {3-x}{2}+1\right ) \]