Internal problem ID [6163]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
Order:=8; dsolve((x^2-2*x+2)*diff(y(x),x$2)-4*(x-1)*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \frac {\left (-x^{3}+3 x^{2}-2\right ) D\relax (y )\relax (1)}{3}-3 y \relax (1) \left (x^{2}-2 x +\frac {2}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 31
AsymptoticDSolveValue[(x^2-2*x+2)*y''[x]-4*(x-1)*y'[x]+6*y[x]==0,y[x],{x,1,7}]
\[ y(x)\to c_1 \left (1-3 (x-1)^2\right )+c_2 \left (-\frac {1}{3} (x-1)^3+x-1\right ) \]