8.3.1 problem 3

Internal problem ID [2510]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.9. Exact equations. Excercises page 66
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 05:39:58 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 19

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

\[ y^{3} {\mathrm e}^{t}+\sin \left (y\right ) t^{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.264 (sec). Leaf size: 22

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

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

✗ Sympy

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

Timed Out