73.1.40 problem 2.7 d

Internal problem ID [15018]
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 : Tuesday, January 28, 2025 at 07:27:38 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*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 20

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

\[ y(x)\to \frac {1}{6} \sqrt {\pi } \text {erf}(3 x)+1 \]