15.4.5 problem 5

Internal problem ID [2918]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 5
Date solved : Sunday, March 30, 2025 at 12:55:21 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.397 (sec). Leaf size: 32

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

\[ \text {Solve}\left [x^3 y(x)+\frac {1}{2} x^2 y(x)^2-\cos (y(x))+e^x=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out