Internal problem ID [13932]
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 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
Order:=6; dsolve((x^2-2*x+2)*diff(y(x),x$2)+(1-x)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=1);
\[ y \left (x \right ) = \left (1+\frac {3 \left (-1+x \right )^{2}}{2}+\frac {3 \left (-1+x \right )^{4}}{8}\right ) y \left (1\right )+\left (-1+x +\frac {2 \left (-1+x \right )^{3}}{3}\right ) D\left (y \right )\left (1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[(x^2-2*x+2)*y''[x]+(1-x)*y'[x]-3*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (\frac {3}{8} (x-1)^4+\frac {3}{2} (x-1)^2+1\right )+c_2 \left (\frac {2}{3} (x-1)^3+x-1\right ) \]