72.7.10 problem 10

Internal problem ID [14751]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 07:13:43 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-2 t y+4 \,{\mathrm e}^{-t^{2}} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

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

\[ y = \left (4 t +3\right ) {\mathrm e}^{-t^{2}} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 18

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

\[ y(t)\to e^{-t^2} (4 t+3) \]