Internal problem ID [1219]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (x -3\right ) y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 34
Order:=6; dsolve(diff(y(x),x$2)-(x-3)*diff(y(x),x)-y(x)=0,y(x),type='series',x=3);
\[ y \relax (x ) = \left (1+\frac {\left (x -3\right )^{2}}{2}+\frac {\left (x -3\right )^{4}}{8}\right ) y \relax (3)+\left (x -3+\frac {\left (x -3\right )^{3}}{3}+\frac {\left (x -3\right )^{5}}{15}\right ) D\relax (y )\relax (3)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 51
AsymptoticDSolveValue[y''[x]-(x-3)*y'[x]-y[x]==0,y[x],{x,3,5}]
\[ y(x)\to c_1 \left (\frac {1}{8} (x-3)^4+\frac {1}{2} (x-3)^2+1\right )+c_2 \left (\frac {1}{15} (x-3)^5+\frac {1}{3} (x-3)^3+x-3\right ) \]