72.8.17 problem 30

Internal problem ID [14781]
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. Review Exercises for chapter 1. page 136
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 07:15:11 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=-x t \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&={\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 12

dsolve([diff(x(t),t)= -t*x(t),x(0) = exp(1)],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{1-\frac {t^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 16

DSolve[{D[x[t],t]==-t*x[t],{x[0]==Exp[1]}},x[t],t,IncludeSingularSolutions -> True]
 

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