63.3.2 problem 2

Internal problem ID [13037]
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 : 2
Date solved : Tuesday, January 28, 2025 at 04:49:54 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\frac {1+t}{\sqrt {t}} \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 16

dsolve([diff(x(t),t)=(1+t)/sqrt(t),x(1) = 4],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {2 t^{{3}/{2}}}{3}+2 \sqrt {t}+\frac {4}{3} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 23

DSolve[{D[x[t],t]==(1+t)/Sqrt[t],{x[1]==4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {2}{3} \left (t^{3/2}+3 \sqrt {t}+2\right ) \]