12.4.6 problem 6

Internal problem ID [1613]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 6
Date solved : Saturday, March 29, 2025 at 11:07:39 PM
CAS classification : [_separable]

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

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

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

\[ y = c_1 \,{\mathrm e}^{x^{2}} \]

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

ode=D[y[x],x]==2*x*y[x]; 
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: 0.230 (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)
 

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