Internal problem ID [11384]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-{\mathrm e}^{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.594 (sec). Leaf size: 17
DSolve[x'[t]==Exp[x[t]^2],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \text {erf}^{-1}\left (\frac {2 (t+c_1)}{\sqrt {\pi }}\right ) \]