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 : Sunday, March 30, 2025 at 10:48:43 AM
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*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 11

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

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

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

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

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

✓ Sympy. Time used: 0.202 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x**2) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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