72.1.22 problem 25

Internal problem ID [14622]
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 1.2. page 33
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 06:44:51 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} x \left (0\right )&=\frac {1}{\sqrt {\pi }} \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 14

dsolve([diff(x(t),t)=-x(t)*t,x(0) = 1/Pi^(1/2)],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 20

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

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