74.5.10 problem 10

Internal problem ID [15903]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 10
Date solved : Monday, March 31, 2025 at 02:12:30 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 31

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

\[ y(t)\to \left (t^2+1\right ) \left (\int _1^t\frac {2}{K[1]^2+1}dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.355 (sec). Leaf size: 42

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

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