74.5.33 problem 33

Internal problem ID [15926]
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 : 33
Date solved : Monday, March 31, 2025 at 02:13:33 PM
CAS classification : [_separable]

\begin{align*} \left (t^{2}+4\right ) y^{\prime }+2 t y&=2 t \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-4 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 17

ode:=(t^2+4)*diff(y(t),t)+2*t*y(t) = 2*t; 
ic:=y(0) = -4; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {t^{2}-16}{t^{2}+4} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 18

ode=(t^2+4)*D[y[t],t]+2*t*y[t]==2*t; 
ic={y[0]==-4}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {t^2-16}{t^2+4} \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 12

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

\[ y{\left (t \right )} = \frac {t^{2} - 16}{t^{2} + 4} \]