50.2.2 problem 1(b)

Internal problem ID [7808]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(b)
Date solved : Wednesday, March 05, 2025 at 05:06:36 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=4 x y \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

ode:=diff(y(x),x) = 4*x*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 20

ode=D[y[x],x]==4*x*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.235 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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