57.3.2 problem 2

Internal problem ID [14318]
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 : Thursday, October 02, 2025 at 09:31:28 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 16

ode:=diff(x(t),t) = (t+1)/t^(1/2); 
ic:=[x(1) = 4]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

\begin{align*} x(t)&\to \frac {2}{3} \left (t^{3/2}+3 \sqrt {t}+2\right ) \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) - (t + 1)/sqrt(t),0) 
ics = {x(1): 4} 
dsolve(ode,func=x(t),ics=ics)
 

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