50.17.1 problem 1(a) solving using series

Internal problem ID [8072]
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
Date solved : Monday, January 27, 2025 at 03:43:09 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 y x \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

Order:=8; 
dsolve(diff(y(x),x)=2*x*y(x),y(x),type='series',x=0);
 

\[ y = \left (1+x^{2}+\frac {1}{2} x^{4}+\frac {1}{6} x^{6}\right ) y \left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 25

AsymptoticDSolveValue[D[y[x],x]==2*x*y[x],y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^6}{6}+\frac {x^4}{2}+x^2+1\right ) \]