78.8.39 problem 39

Internal problem ID [18166]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 39
Date solved : Monday, March 31, 2025 at 05:20:47 PM
CAS classification : [_linear]

\begin{align*} {\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=exp(x^2*y(x))*(1+2*x^2*y(x))+x^3*exp(x^2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (-\frac {c_1}{x}\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 16

ode=Exp[x^2*y[x]]*(1+2*x^2*y[x])+ x^3*Exp[x^2*y[x]] * D[y[x],x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-\log (x)+c_1}{x^2} \]

✓ Sympy. Time used: 0.270 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*exp(x**2*y(x))*Derivative(y(x), x) + (2*x**2*y(x) + 1)*exp(x**2*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - \log {\left (x \right )}}{x^{2}} \]