Internal problem ID [434]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.2 Power series solutions. Page 624
Problem number: problem 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0, y^{\prime }\relax (1) = 1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 14
Order:=6; dsolve([(2*x-x^2)*diff(y(x),x$2)-6*(x-1)*diff(y(x),x)-4*y(x)=0,y(1) = 0, D(y)(1) = 1],y(x),type='series',x=1);
\[ y \relax (x ) = \left (x -1\right )+\frac {5}{3} \left (x -1\right )^{3}+\frac {7}{3} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 24
AsymptoticDSolveValue[{(2*x-x^2)*y''[x]-6*(x-1)*y'[x]-4*y[x]==0,{y[1]==0,y'[1]==1}},y[x],{x,1,5}]
\[ y(x)\to \frac {7}{3} (x-1)^5+\frac {5}{3} (x-1)^3+x-1 \]