Internal problem ID [1290]
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: 48.
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}+x \right ) y^{\prime \prime }+\left (-x^{2}+3 x +1\right ) y^{\prime }+\left (2+x \right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 0] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
Order:=6; dsolve([(x-2*x^2)*diff(y(x),x$2)+(1+3*x-x^2)*diff(y(x),x)+(2+x)*y(x)=0,y(1) = 1, D(y)(1) = 0],y(x),type='series',x=1);
\[ y \relax (x ) = 1+\frac {3}{2} \left (x -1\right )^{2}+\frac {1}{6} \left (x -1\right )^{3}-\frac {1}{8} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 32
AsymptoticDSolveValue[{(x-2*x^2)*y''[x]+(1+3*x-x^2)*y'[x]+(2+x)*y[x]==0,{y[1]==1,y'[1]==0}},y[x],{x,1,5}]
\[ y(x)\to -\frac {1}{8} (x-1)^5+\frac {1}{6} (x-1)^3+\frac {3}{2} (x-1)^2+1 \]