76.2.7 problem 7

Internal problem ID [17343]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 10:01:49 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 t y&=16 t \,{\mathrm e}^{-t^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve(diff(y(t),t)+2*t*y(t)=16*t*exp(-t^2),y(t), singsol=all)
 

\[ y = \left (8 t^{2}+c_{1} \right ) {\mathrm e}^{-t^{2}} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 21

DSolve[D[y[t],t]+2*t*y[t]==16*t*Exp[-t^2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t^2} \left (8 t^2+c_1\right ) \]