Internal problem ID [435]
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 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = 2, y^{\prime }\relax (3) = 0] \end {align*}
With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
Order:=6; dsolve([(x^2-6*x+10)*diff(y(x),x$2)-4*(x-3)*diff(y(x),x)+6*y(x)=0,y(3) = 2, D(y)(3) = 0],y(x),type='series',x=3);
\[ y \relax (x ) = -6 x^{2}+36 x -52 \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 12
AsymptoticDSolveValue[{(x^2-6*x+10)*y''[x]-4*(x-3)*y'[x]+6*y[x]==0,{y[3]==2,y'[3]==0}},y[x],{x,3,5}]
\[ y(x)\to 2-6 (x-3)^2 \]