63.4.7 problem 1(g)

Internal problem ID [13050]
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 : Tuesday, January 28, 2025 at 04:50:12 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 14

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

\[ t -\frac {\sqrt {\pi }\, \operatorname {erf}\left (x \left (t \right )\right )}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.351 (sec). Leaf size: 17

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

\[ x(t)\to \text {erf}^{-1}\left (\frac {2 (t+c_1)}{\sqrt {\pi }}\right ) \]