Internal problem ID [1285]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime \prime }+\left (2 x^{2}-3 x +1\right ) y^{\prime }-\left (x -4\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -2, y^{\prime }\relax (1) = 3] \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+x)*diff(y(x),x$2)+(1-3*x+2*x^2)*diff(y(x),x)-(x-4)*y(x)=0,y(1) = -2, D(y)(1) = 3],y(x),type='series',x=1);
\[ y \relax (x ) = -2+3 \left (x -1\right )+\frac {3}{2} \left (x -1\right )^{2}-\frac {17}{12} \left (x -1\right )^{3}-\frac {1}{12} \left (x -1\right )^{4}+\frac {1}{8} \left (x -1\right )^{5}+\mathrm {O}\left (\left (x -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 46
AsymptoticDSolveValue[{(1+x)*y''[x]+(1-3*x+x^2)*y'[x]-(x-4)*y[x]==0,{y[1]==-2,y'[1]==3}},y[x],{x,1,5}]
\[ y(x)\to -\frac {13}{240} (x-1)^5-\frac {1}{96} (x-1)^4-\frac {2}{3} (x-1)^3+\frac {9}{4} (x-1)^2+3 (x-1)-2 \]