Internal problem ID [14778]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y=0} \] With the expansion point for the power series method at \(x = -2\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
Order:=6; dsolve((x-2)*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(x),type='series',x=-2);
\[ y \left (x \right ) = \left (1-\frac {\left (x +2\right )^{2}}{8}-\frac {\left (x +2\right )^{3}}{48}-\frac {\left (x +2\right )^{4}}{768}\right ) y \left (-2\right )+\left (x +2+\frac {\left (x +2\right )^{2}}{8}-\frac {\left (x +2\right )^{3}}{48}-\frac {5 \left (x +2\right )^{4}}{768}-\frac {\left (x +2\right )^{5}}{960}\right ) D\left (y \right )\left (-2\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 78
AsymptoticDSolveValue[(x-2)*y''[x]+y'[x]-y[x]==0,y[x],{x,-2,5}]
\[ y(x)\to c_1 \left (-\frac {1}{768} (x+2)^4-\frac {1}{48} (x+2)^3-\frac {1}{8} (x+2)^2+1\right )+c_2 \left (-\frac {1}{960} (x+2)^5-\frac {5}{768} (x+2)^4-\frac {1}{48} (x+2)^3+\frac {1}{8} (x+2)^2+x+2\right ) \]