Internal problem ID [1227]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (4) = 3, y^{\prime }\relax (4) = -4] \end {align*}
With the expansion point for the power series method at \(x = 4\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
Order:=6; dsolve([(x^2-8*x+14)*diff(y(x),x$2)-8*(x-4)*diff(y(x),x)+20*y(x)=0,y(4) = 3, D(y)(4) = -4],y(x),type='series',x=4);
\[ y \relax (x ) = 3-4 \left (x -4\right )+15 \left (x -4\right )^{2}-4 \left (x -4\right )^{3}+\frac {15}{4} \left (x -4\right )^{4}-\frac {1}{5} \left (x -4\right )^{5}+\mathrm {O}\left (\left (x -4\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 44
AsymptoticDSolveValue[{(x^2-8*x+14)*y''[x]+8*(x-4)*y'[x]+20*y[x]==0,{y[4]==3,y'[4]==-4}},y[x],{x,4,5}]
\[ y(x)\to -\frac {35}{3} (x-4)^5+\frac {95}{4} (x-4)^4-\frac {28}{3} (x-4)^3+15 (x-4)^2-4 (x-4)+3 \]