44.4.11 problem 3 (c)

Internal problem ID [7024]
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 (c)
Date solved : Monday, January 27, 2025 at 02:41:16 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 43

dsolve([diff(y(x),x)=1-x*y(x),y(2) = 2],y(x), singsol=all)
 

\[ y = -\frac {\left (i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )+\operatorname {erfi}\left (\sqrt {2}\right ) \sqrt {2}\, \sqrt {\pi }-4 \,{\mathrm e}^{2}\right ) {\mathrm e}^{-\frac {x^{2}}{2}}}{2} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 55

DSolve[{D[y[x],x]==1-x*y[x],{y[2]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } \text {erfi}\left (\frac {x}{\sqrt {2}}\right )-\sqrt {2 \pi } \text {erfi}\left (\sqrt {2}\right )+4 e^2\right ) \]