72.7.4 problem 4

Internal problem ID [14745]
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 : 4
Date solved : Tuesday, January 28, 2025 at 07:13:30 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \left (4 t +c_{1} \right ) {\mathrm e}^{-t^{2}} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 19

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

\[ y(t)\to e^{-t^2} (4 t+c_1) \]