17.1.5 problem 1.1-2 (e)

Internal problem ID [3422]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-2, page 6
Problem number : 1.1-2 (e)
Date solved : Tuesday, March 04, 2025 at 04:38:17 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {t}{t^{2}+4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(y(t),t) = t/(t^2+4); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\ln \left (t^{2}+4\right )}{2}+c_{1} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 18

ode=D[y[t],t]==t/(t^2+4); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{2} \log \left (t^2+4\right )+c_1 \]

✓ Sympy. Time used: 0.146 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t/(t**2 + 4) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + \frac {\log {\left (t^{2} + 4 \right )}}{2} \]