67.1.40 problem 2.7 d

Internal problem ID [16305]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.7 d
Date solved : Thursday, October 02, 2025 at 10:45:33 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{-9 x^{2}} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.051 (sec). Leaf size: 15

ode:=diff(y(x),x) = exp(-9*x^2); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sqrt {\pi }\, \operatorname {erf}\left (3 x \right )}{6}+1 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=D[y[x],x]==Exp[-9*x^2]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} \sqrt {\pi } \text {erf}(3 x)+1 \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - exp(-9*x**2),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt {\pi } \operatorname {erf}{\left (3 x \right )}}{6} + 1 \]