78.17.1 problem 1 (a)

Internal problem ID [18336]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 27. Series Solutions of First Order Equations. Problems at page 208
Problem number : 1 (a)
Date solved : Monday, March 31, 2025 at 05:25:51 PM
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: 0.004 (sec). Leaf size: 22

Order:=6; 
ode:=diff(y(x),x) = 2*x*y(x); 
dsolve(ode,y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=D[y[x],x]==2*x*y[x]; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

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

✓ Sympy. Time used: 0.652 (sec). Leaf size: 19

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=6)
 

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