72.7.5 problem 5

Internal problem ID [14675]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 5
Date solved : Monday, March 31, 2025 at 12:52:28 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {2 t y}{t^{2}+1}&=3 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(t),t)-2*t/(t^2+1)*y(t) = 3; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (3 \arctan \left (t \right )+c_1 \right ) \left (t^{2}+1\right ) \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 31

ode=D[y[t],t]-2*t/(1+t^2)*y[t]==3; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \left (t^2+1\right ) \left (\int _1^t\frac {3}{K[1]^2+1}dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.381 (sec). Leaf size: 56

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*t*y(t)/(t**2 + 1) + Derivative(y(t), t) - 3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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