50.1.16 problem 2(b)

Internal problem ID [7788]
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 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 2(b)
Date solved : Wednesday, March 05, 2025 at 05:06:03 AM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 17

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

\[ y(x)\to \frac {e^{x^2}}{2}+c_1 \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(x**2) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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