Internal problem ID [1264]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (10-2 x \right ) y^{\prime \prime }+\left (x +1\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 2, y^{\prime }\relax (2) = -4] \end {align*}
With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(10-2*x)*diff(y(x),x$2)+(1+x)*y(x)=0,y(2) = 2, D(y)(2) = -4],y(x),type='series',x=2);
\[ y \relax (x ) = 2-4 \left (-2+x \right )-\frac {1}{2} \left (-2+x \right )^{2}+\frac {2}{9} \left (-2+x \right )^{3}+\frac {49}{432} \left (-2+x \right )^{4}+\frac {23}{1080} \left (-2+x \right )^{5}+\mathrm {O}\left (\left (-2+x \right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 46
AsymptoticDSolveValue[{(10-2*x)*y''[x]+(1+x)*y[x]==0,{y[2]==2,y'[2]==-4}},y[x],{x,2,5}]
\[ y(x)\to \frac {23 (x-2)^5}{1080}+\frac {49}{432} (x-2)^4+\frac {2}{9} (x-2)^3-\frac {1}{2} (x-2)^2-4 (x-2)+2 \]