11.6.8 problem 1.2-1 (h)

Internal problem ID [3445]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (h)
Date solved : Tuesday, September 30, 2025 at 06:38:34 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {2 t y}{t^{2}+1}+t +1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

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

\[ y = \left (\frac {\ln \left (t^{2}+1\right )}{2}+\arctan \left (t \right )+c_1 \right ) \left (t^{2}+1\right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 26

ode=D[y[t],t]==2*t/(t^2+1)*y[t]+t+1; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \left (t^2+1\right ) \left (\arctan (t)+\frac {1}{2} \log \left (t^2+1\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.335 (sec). Leaf size: 53

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t - 2*t*y(t)/(t**2 + 1) + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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