Internal problem ID [13598]
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 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (1-x \right ) y^{\prime }-2 y=0} \] With the expansion point for the power series method at \(x = 5\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
Order:=6; dsolve((1-x)*diff(y(x),x)-2*y(x)=0,y(x),type='series',x=5);
\[ y \left (x \right ) = \left (\frac {7}{2}-\frac {x}{2}+\frac {3 \left (x -5\right )^{2}}{16}-\frac {\left (x -5\right )^{3}}{16}+\frac {5 \left (x -5\right )^{4}}{256}-\frac {3 \left (x -5\right )^{5}}{512}\right ) y \left (5\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 53
AsymptoticDSolveValue[(1-x)*y'[x]-2*y[x]==0,y[x],{x,5,5}]
\[ y(x)\to c_1 \left (-\frac {3}{512} (x-5)^5+\frac {5}{256} (x-5)^4-\frac {1}{16} (x-5)^3+\frac {3}{16} (x-5)^2+\frac {5-x}{2}+1\right ) \]