38.4.10 problem 3 (b)

Internal problem ID [8309]
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 : Tuesday, September 30, 2025 at 05:22:32 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.113 (sec). Leaf size: 32

ode:=diff(y(x),x) = 1-x*y(x); 
ic:=[y(-1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 39

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

\begin{align*} 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 ) \end{align*}

✓ Sympy. Time used: 0.251 (sec). Leaf size: 51

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

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