10.6.18 problem 18

Internal problem ID [1235]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 18
Date solved : Saturday, March 29, 2025 at 10:49:24 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \end{align*}

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

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

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

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.844 (sec). Leaf size: 19

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

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