63.4.1 problem 1(a)

Internal problem ID [13044]
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(a)
Date solved : Tuesday, January 28, 2025 at 04:50:03 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\sqrt {x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.077 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

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

\[ x(t)\to \frac {2 t^{3/2}}{3}+1 \]