36.1.30 problem 28

Internal problem ID [6285]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 28
Date solved : Monday, January 27, 2025 at 01:54:38 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 13

dsolve([diff(y(t),t)=2*y(t)-2*t*y(t),y(0) = 3],y(t), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{-t \left (t -2\right )} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 15

DSolve[{D[y[t],t]==2*y[t]-2*t*y[t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 e^{-((t-2) t)} \]