63.3.7 problem 6

Internal problem ID [13042]
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
Date solved : Tuesday, January 28, 2025 at 04:50:00 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\frac {{\mathrm e}^{-t}}{\sqrt {t}} \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 17

dsolve([diff(x(t),t)=exp(-t)/sqrt(t),x(1) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \left (\operatorname {erf}\left (\sqrt {t}\right )-\operatorname {erf}\left (1\right )\right ) \sqrt {\pi } \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 22

DSolve[{D[x[t],t]==Exp[-t]/Sqrt[t],{x[1]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sqrt {\pi } \left (\text {erf}\left (\sqrt {t}\right )-\text {erf}(1)\right ) \]