Internal problem ID [4518]
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: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 x y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
Order:=6; dsolve(diff(y(x),x)-2*x*y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (-1+2 x +3 \left (x -1\right )^{2}+\frac {10 \left (x -1\right )^{3}}{3}+\frac {19 \left (x -1\right )^{4}}{6}+\frac {13 \left (x -1\right )^{5}}{5}\right ) y \relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 47
AsymptoticDSolveValue[y'[x]-2*x*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (\frac {13}{5} (x-1)^5+\frac {19}{6} (x-1)^4+\frac {10}{3} (x-1)^3+3 (x-1)^2+2 (x-1)+1\right ) \]