72.1.22 problem 25

Internal problem ID [14543]
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 : Thursday, March 13, 2025 at 03:33:11 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*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.259 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t*x(t) + Derivative(x(t), t),0) 
ics = {x(0): 1/sqrt(pi)} 
dsolve(ode,func=x(t),ics=ics)
 

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