68.5.11 problem 11

Internal problem ID [17262]
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 : 11
Date solved : Thursday, October 02, 2025 at 02:00:10 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(y(t),t)-4*t/(4*t^2+1)*y(t) = 4*t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = 4 t^{2}+1+\sqrt {4 t^{2}+1}\, c_1 \]

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

ode=D[y[t],t]-4*t/(1+4*t^2)*y[t]==4*t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 4 t^2+c_1 \sqrt {4 t^2+1}+1 \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*t - 4*t*y(t)/(4*t**2 + 1) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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