71.2.1 problem 1

Internal problem ID [14254]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 1
Date solved : Wednesday, March 05, 2025 at 10:41:29 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-2 x y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(x),x)-2*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x^{2}} c_{1} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 18

ode=D[y[x],x]-2*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 e^{x^2} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.237 (sec). Leaf size: 8

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)
 

\[ y{\left (x \right )} = C_{1} e^{x^{2}} \]