Internal problem ID [1291]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.3 SERIES SOLUTIONS NEAR AN
ORDINARY POINT II. Exercises 7.3. Page 338
Problem number: 49.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (2-x \right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = 1, y^{\prime }\relax (3) = -2] \end {align*}
With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(16-11*x+2*x^2)*diff(y(x),x$2)+(10-6*x+x^2)*diff(y(x),x)-(2-x)*y(x)=0,y(3) = 1, D(y)(3) = -2],y(x),type='series',x=3);
\[ y \relax (x ) = 1-2 \left (x -3\right )+\frac {1}{2} \left (x -3\right )^{2}-\frac {1}{6} \left (x -3\right )^{3}+\frac {1}{4} \left (x -3\right )^{4}-\frac {1}{6} \left (x -3\right )^{5}+\mathrm {O}\left (\left (x -3\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 46
AsymptoticDSolveValue[{(16-11*x+2*x^2)*y''[x]+(10-6*x+x^2)*y'[x]-(2-x)*y[x]==0,{y[3]==1,y'[3]==-2}},y[x],{x,3,5}]
\[ y(x)\to -\frac {1}{6} (x-3)^5+\frac {1}{4} (x-3)^4-\frac {1}{6} (x-3)^3+\frac {1}{2} (x-3)^2-2 (x-3)+1 \]