74.5.33 problem 33

Internal problem ID [15997]
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 : Tuesday, January 28, 2025 at 08:26:04 AM
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*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

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

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

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