44.4.10 problem 3 (b)

Internal problem ID [7023]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 3 (b)
Date solved : Monday, January 27, 2025 at 02:41:14 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1-y x \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 32

dsolve([diff(y(x),x)=1-x*y(x),y(-1) = 0],y(x), singsol=all)
 

\[ y = -\frac {i \sqrt {\pi }\, \sqrt {2}\, \left (\operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )+\operatorname {erf}\left (\frac {i \sqrt {2}}{2}\right )\right ) {\mathrm e}^{-\frac {x^{2}}{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 39

DSolve[{D[y[x],x]==1-x*y[x],{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {\frac {\pi }{2}} e^{-\frac {x^2}{2}} \left (\text {erfi}\left (\frac {x}{\sqrt {2}}\right )+\text {erfi}\left (\frac {1}{\sqrt {2}}\right )\right ) \]