73.1.37 problem 2.7 a

Internal problem ID [15015]
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 : Tuesday, January 28, 2025 at 07:27:34 AM
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*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

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

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

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