Internal problem ID [4871]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page
174
Problem number: 7.
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 \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
Order:=6; dsolve(diff(y(x),x)=-2*x*y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-x^{2}+\frac {1}{2} x^{4}\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 20
AsymptoticDSolveValue[y'[x]==-2*x*y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{2}-x^2+1\right ) \]