44.5.31 problem 31

Internal problem ID [7093]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 08:48:55 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (4\right )&=1 \end{align*}

Solution by Maple

Time used: 0.036 (sec). Leaf size: 17

dsolve([diff(y(x),x)=y(x)*exp(-x^2),y(4) = 1],y(x), singsol=all)
 
\[ y = {\mathrm e}^{\frac {\left (-\operatorname {erf}\left (4\right )+\operatorname {erf}\left (x \right )\right ) \sqrt {\pi }}{2}} \]

Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 23

DSolve[{D[y[x],x]==y[x]*Exp[-x^2],{y[4]==1}},y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^{\frac {1}{2} \sqrt {\pi } (\text {erf}(x)-\text {erf}(4))} \]