78.1.17 problem 2 (c)

Internal problem ID [18072]
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 : Tuesday, January 28, 2025 at 11:25:28 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 17

DSolve[D[y[x],x]==x*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
 

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