Internal problem ID [4503]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.3. page 443
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\left (2+x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 36
Order:=6; dsolve(diff(y(x),x)+(x+2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-2 x +\frac {3}{2} x^{2}-\frac {1}{3} x^{3}-\frac {5}{24} x^{4}+\frac {3}{20} x^{5}\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 39
AsymptoticDSolveValue[y'[x]+(x+2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {3 x^5}{20}-\frac {5 x^4}{24}-\frac {x^3}{3}+\frac {3 x^2}{2}-2 x+1\right ) \]