74.5.28 problem 28

Internal problem ID [15992]
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 : 28
Date solved : Tuesday, January 28, 2025 at 08:25:53 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+3 t^{2} y&={\mathrm e}^{-t^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 16

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

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