16.1.4 problem 2(d)

Internal problem ID [3406]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 2(d)
Date solved : Monday, January 27, 2025 at 07:35:52 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

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

\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \operatorname {erfi}\left (x \right )}{2}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{2} \sqrt {\pi } \text {erfi}(x)+c_1 \]