Internal problem ID [4522]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
Order:=6; dsolve(diff(y(x),x$2)+(3*x-1)*diff(y(x),x)-y(x)=0,y(x),type='series',x=-1);
\[ y \relax (x ) = \left (1+\frac {\left (x +1\right )^{2}}{2}+\frac {2 \left (x +1\right )^{3}}{3}+\frac {11 \left (x +1\right )^{4}}{24}+\frac {\left (x +1\right )^{5}}{10}\right ) y \left (-1\right )+\left (x +1+2 \left (x +1\right )^{2}+\frac {7 \left (x +1\right )^{3}}{3}+\frac {3 \left (x +1\right )^{4}}{2}+\frac {4 \left (x +1\right )^{5}}{15}\right ) D\relax (y )\left (-1\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 85
AsymptoticDSolveValue[y''[x]+(3*x-1)*y'[x]-y[x]==0,y[x],{x,-1,5}]
\[ y(x)\to c_1 \left (\frac {1}{10} (x+1)^5+\frac {11}{24} (x+1)^4+\frac {2}{3} (x+1)^3+\frac {1}{2} (x+1)^2+1\right )+c_2 \left (\frac {4}{15} (x+1)^5+\frac {3}{2} (x+1)^4+\frac {7}{3} (x+1)^3+2 (x+1)^2+x+1\right ) \]