23.1.431 problem 421

Internal problem ID [5038]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 421
Date solved : Tuesday, September 30, 2025 at 11:28:27 AM
CAS classification : [_separable]

\begin{align*} y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

ode:=y(x)*diff(y(x),x)+x*exp(x^2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-{\mathrm e}^{x^{2}}+c_1} \\ y &= -\sqrt {-{\mathrm e}^{x^{2}}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 1.69 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to -\sqrt {-e^{x^2}+2 c_1}\\ y(x)&\to \sqrt {-e^{x^2}+2 c_1} \end{align*}

✓ Sympy. Time used: 0.242 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - e^{x^{2}}}, \ y{\left (x \right )} = \sqrt {C_{1} - e^{x^{2}}}\right ] \]