74.5.14 problem 14

Internal problem ID [15978]
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 : Tuesday, January 28, 2025 at 08:25:24 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 24

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

\[ y(t)\to -t^2+c_1 \left (t^2-4\right )^{3/2}+4 \]