Internal problem ID [433]
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 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 0] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 14
Order:=6; dsolve([diff(y(x),x$2)+(x-1)*diff(y(x),x)+y(x)=0,y(1) = 2, D(y)(1) = 0],y(x),type='series',x=1);
\[ y \relax (x ) = 2-\left (x -1\right )^{2}+\frac {1}{4} \left (x -1\right )^{4}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 21
AsymptoticDSolveValue[{y''[x]+(x-1)*y'[x]+y[x]==0,{y[1]==2,y'[1]==0}},y[x],{x,1,5}]
\[ y(x)\to \frac {1}{4} (x-1)^4-(x-1)^2+2 \]