87.2.1 problem 1

Internal problem ID [23236]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:24:51 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y x&=3 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 27

ode:=diff(y(x),x)+x*y(x) = 3; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3 i {\mathrm e}^{-\frac {x^{2}}{2}} \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right )}{2} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 33

ode=D[y[x],x]+x*y[x]==3; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 \sqrt {\frac {\pi }{2}} e^{-\frac {x^2}{2}} \text {erfi}\left (\frac {x}{\sqrt {2}}\right ) \end{align*}

✓ Sympy. Time used: 0.256 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x) + Derivative(y(x), x) - 3,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 \sqrt {2} \sqrt {\pi } e^{- \frac {x^{2}}{2}} \operatorname {erfi}{\left (\frac {\sqrt {2} x}{2} \right )}}{2} \]