68.5.14 problem 14

Internal problem ID [17265]
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 : 14
Date solved : Thursday, October 02, 2025 at 02:00:18 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {3 t y}{t^{2}-4}&=t \end{align*}

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

ode:=diff(y(t),t)-3*t/(t^2-4)*y(t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (t -2\right ) \left (t +2\right ) \left (\sqrt {t^{2}-4}\, c_1 -1\right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 24

ode=D[y[t],t]-3*t/(t^2-4)*y[t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -t^2+c_1 \left (t^2-4\right )^{3/2}+4 \end{align*}

✓ Sympy. Time used: 0.503 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t - 3*t*y(t)/(t**2 - 4) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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