28.1.136 problem 159

Internal problem ID [4442]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 159
Date solved : Tuesday, March 04, 2025 at 06:44:06 PM
CAS classification : [`x=_G(y,y')`]

\begin{align*} 2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-x^{2} y^{2}-3 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 35

ode:=2*x*y(x)^4*exp(y(x))+2*x*y(x)^3+y(x)+(x^2*y(x)^4*exp(y(x))-x^2*y(x)^2-3*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.308 (sec). Leaf size: 29

ode=(2*x*y[x]^4*Exp[y[x]]+2*x*y[x]^3+y[x])+(x^2*y[x]^4*Exp[y[x]]-x^2*y[x]^2-3*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**4*exp(y(x)) + 2*x*y(x)**3 + (x**2*y(x)**4*exp(y(x)) - x**2*y(x)**2 - 3*x)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out