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 : Wednesday, March 05, 2025 at 05:29:13 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

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

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

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

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

ode=D[y[x],x]==2*x*y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

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

✓ Sympy. Time used: 0.667 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="1st_power_series",x0=0,n=8)
 

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