8.6.4 problem 4

Internal problem ID [774]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 4
Date solved : Saturday, March 29, 2025 at 10:22:00 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 20

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

\[ x^{2} y^{3}+{\mathrm e}^{x}-\cos \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 23

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

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

✗ Sympy

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

Timed Out