68.5.15 problem 15

Internal problem ID [17266]
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 : 15
Date solved : Thursday, October 02, 2025 at 02:00:20 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}-9}&=t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(t),t)-4*t/(4*t^2-9)*y(t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = t^{2}-\frac {9}{4}+\sqrt {4 t^{2}-9}\, c_1 \]

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

ode=D[y[t],t]-4*t/(4*t^2-9)*y[t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t^2+c_1 \sqrt {4 t^2-9}-\frac {9}{4} \end{align*}

✓ Sympy. Time used: 0.263 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t - 4*t*y(t)/(4*t**2 - 9) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} \sqrt {4 t^{2} - 9} + t^{2} - \frac {9}{4} \]