44.4.12 problem 3 (d)

Internal problem ID [7025]
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 (d)
Date solved : Monday, January 27, 2025 at 02:41:18 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 29

dsolve([diff(y(x),x)=1-x*y(x),y(0) = -4],y(x), singsol=all)
 

\[ y = -\frac {\left (i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )+8\right ) {\mathrm e}^{-\frac {x^{2}}{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 36

DSolve[{D[y[x],x]==1-x*y[x],{y[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-8\right ) \]