78.1.17 problem 2 (c)

Internal problem ID [18001]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (c)
Date solved : Monday, March 31, 2025 at 04:56:08 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (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: 0.016 (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: 0.147 (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)
 

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