61.1.8 problem Problem 1(h)

Internal problem ID [15236]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(h)
Date solved : Thursday, October 02, 2025 at 10:07:45 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 22

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

\[ -\left (x +1\right ) {\mathrm e}^{-x}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (y\right )}{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.437 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.167 (sec). Leaf size: 27

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

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