Internal problem ID [10348]
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 1.2 Antiderivatives. Exercises page
19
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-\frac {{\mathrm e}^{-t}}{\sqrt {t}}=0} \] With initial conditions \begin {align*} [x \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 20
dsolve([diff(x(t),t)=exp(-t)/sqrt(t),x(1) = 0],x(t), singsol=all)
\[ x \left (t \right ) = -\left (\operatorname {erf}\left (1\right )-\operatorname {erf}\left (\sqrt {t}\right )\right ) \sqrt {\pi } \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[{x'[t]==Exp[-t]/Sqrt[t],{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \sqrt {\pi } \left (\text {erf}\left (\sqrt {t}\right )-\text {erf}(1)\right ) \\ \end{align*}