20.5.4 problem Problem 4

Internal problem ID [3687]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number : Problem 4
Date solved : Sunday, March 30, 2025 at 02:05:46 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

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

\[ x^{2} {\mathrm e}^{y}+y^{3}+c_1 = 0 \]

✓ Mathematica. Time used: 0.26 (sec). Leaf size: 19

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

\[ \text {Solve}\left [x^2 e^{y(x)}+y(x)^3=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.850 (sec). Leaf size: 19

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

\[ C_{1} + \frac {x^{2} e^{y{\left (x \right )}}}{2} + \frac {y^{3}{\left (x \right )}}{2} = 0 \]