73.1.37 problem 2.7 a

Internal problem ID [14944]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.7 a
Date solved : Monday, March 31, 2025 at 01:04:38 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 14

ode:=diff(y(x),x) = x*exp(-x^2); 
ic:=y(0) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-x^{2}}}{2}+\frac {7}{2} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 20

ode=D[y[x],x]==x*Exp[-x^2]; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {7}{2}-\frac {e^{-x^2}}{2} \]

✓ Sympy. Time used: 0.183 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(-x**2) + Derivative(y(x), x),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {7}{2} - \frac {e^{- x^{2}}}{2} \]