16.1.5 problem 2(e)

Internal problem ID [3407]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 2(e)
Date solved : Monday, January 27, 2025 at 07:35:52 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

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

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

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