74.5.29 problem 29

Internal problem ID [15993]
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 : 29
Date solved : Tuesday, January 28, 2025 at 08:25:56 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

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

\[ y = 1-2 \,{\mathrm e}^{-t^{2}} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 16

DSolve[{D[y[t],t]+2*t*y[t]==2*t,{y[0]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 1-2 e^{-t^2} \]