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 : Wednesday, March 05, 2025 at 04:02:42 AM
CAS classification : [_linear]

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

With initial conditions

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

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

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

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

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

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

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

✓ Sympy. Time used: 0.475 (sec). Leaf size: 54

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + Derivative(y(x), x) - 1,0) 
ics = {y(2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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