Internal problem ID [395]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series.
Page 615
Problem number: problem 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+2 y x=0} \] 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)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x^{2}+\frac {1}{2} x^{4}\right ) y \left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 20
AsymptoticDSolveValue[y'[x]+2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{2}-x^2+1\right ) \]