74.3.25 problem 20

Internal problem ID [15885]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 08:17:16 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.542 (sec). Leaf size: 35

dsolve([(t-2)*diff(y(t),t)+(t^2-4)*y(t)=1/(t+2),y(0) = 3],y(t), singsol=all)
 

\[ y = \left (\int _{0}^{t}\frac {{\mathrm e}^{\frac {\textit {\_z1} \left (\textit {\_z1} +4\right )}{2}}}{\textit {\_z1}^{2}-4}d \textit {\_z1} +3\right ) {\mathrm e}^{-\frac {t \left (4+t \right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.269 (sec). Leaf size: 46

DSolve[{(t-2)*D[y[t],t]+(t^2-4)*y[t]==1/(t+2),{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-\frac {1}{2} t (t+4)} \left (\int _0^t\frac {e^{\frac {1}{2} K[1] (K[1]+4)}}{K[1]^2-4}dK[1]+3\right ) \]