Internal problem ID [5651]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 1(a) solving using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
Order:=8; dsolve(diff(y(x),x)=2*x*y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+x^{2}+\frac {1}{2} x^{4}+\frac {1}{6} x^{6}\right ) y \relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 25
AsymptoticDSolveValue[y'[x]==2*x*y[x],y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x^6}{6}+\frac {x^4}{2}+x^2+1\right ) \]