Internal problem ID [1258]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1+2 x \right ) y^{\prime \prime }-\left (1-2 x \right ) y^{\prime }-\left (-2 x +3\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = -2] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 20
Order:=6; dsolve([(1+2*x)*diff(y(x),x$2)-(1-2*x)*diff(y(x),x)-(3-2*x)*y(x)=0,y(1) = 1, D(y)(1) = -2],y(x),type='series',x=1);
\[ y \relax (x ) = 1-2 \left (x -1\right )+\frac {1}{2} \left (x -1\right )^{2}-\frac {1}{6} \left (x -1\right )^{3}+\frac {5}{36} \left (x -1\right )^{4}-\frac {73}{1080} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 46
AsymptoticDSolveValue[{(1+2*x)*y''[x]-(1-2*x)*y'[x]-(3-2*x)*y[x]==0,{y[1]==1,y'[1]==-2}},y[x],{x,1,5}]
\[ y(x)\to -\frac {73 (x-1)^5}{1080}+\frac {5}{36} (x-1)^4-\frac {1}{6} (x-1)^3+\frac {1}{2} (x-1)^2-2 (x-1)+1 \]