36.1.27 problem 27 part(a)

Internal problem ID [6282]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 27 part(a)
Date solved : Monday, January 27, 2025 at 01:53:12 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 11

dsolve([diff(y(x),x)=exp(x^2),y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

DSolve[{D[y[x],x]==Exp[x^2],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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