78.1.45 problem 5

Internal problem ID [18029]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 5
Date solved : Monday, March 31, 2025 at 04:57:14 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=2 x y+1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(x),x) = 2*x*y(x)+1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} e^{x^2} \left (\sqrt {\pi } \text {erf}(x)+2 c_1\right ) \]

✓ Sympy. Time used: 0.305 (sec). Leaf size: 19

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

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