57.4.7 problem 1(g)

Internal problem ID [14331]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 1(g)
Date solved : Thursday, October 02, 2025 at 09:31:39 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 14

ode:=diff(x(t),t) = exp(x(t)^2); 
dsolve(ode,x(t), singsol=all);
 

\[ t -\frac {\sqrt {\pi }\, \operatorname {erf}\left (x\right )}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 17

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

\begin{align*} x(t)&\to \text {erf}^{-1}\left (\frac {2 (t+c_1)}{\sqrt {\pi }}\right ) \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 14

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

\[ x{\left (t \right )} = \operatorname {erfinv}{\left (C_{1} + \frac {2 t}{\sqrt {\pi }} \right )} \]