67.3.25 problem 4.6 (e)

Internal problem ID [16346]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.6 (e)
Date solved : Thursday, October 02, 2025 at 01:21:58 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

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

\[ {\mathrm e}^{x}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (y\right )}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.296 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.162 (sec). Leaf size: 15

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

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