17.1.7 problem 1.1-2 (g)

Internal problem ID [3424]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-2, page 6
Problem number : 1.1-2 (g)
Date solved : Tuesday, March 04, 2025 at 04:38:19 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=diff(y(t),t) = t/(t^(1/2)+1); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2 t^{{3}/{2}}}{3}-t +2 \sqrt {t}-2 \ln \left (\sqrt {t}+1\right )+c_{1} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 25

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

\[ y(t)\to 2 \sqrt {t}-2 \log \left (\sqrt {t}+1\right )+c_1 \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 31

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

\[ y{\left (t \right )} = C_{1} + \frac {2 t^{\frac {3}{2}}}{3} + 2 \sqrt {t} - t - 2 \log {\left (\sqrt {t} + 1 \right )} \]