84.6.2 problem 3.9

Internal problem ID [22103]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Supplementary problems
Problem number : 3.9
Date solved : Thursday, October 02, 2025 at 08:24:55 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(y(x),x) = x*y(x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, x}{2}\right )+2 c_1 \right ) {\mathrm e}^{\frac {x^{2}}{2}}}{2} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {1}{2} e^{\frac {x^2}{2}} \left (\sqrt {2 \pi } \text {erf}\left (\frac {x}{\sqrt {2}}\right )+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.232 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = \left (C_{1} + \frac {\sqrt {2} \sqrt {\pi } \operatorname {erf}{\left (\frac {\sqrt {2} x}{2} \right )}}{2}\right ) e^{\frac {x^{2}}{2}} \]