13.4.6 problem 8

Internal problem ID [2343]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.9. Page 66
Problem number : 8
Date solved : Saturday, March 29, 2025 at 11:57:11 PM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.205 (sec). Leaf size: 23

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

\[ y = \operatorname {RootOf}\left (-2 \textit {\_Z} \,t^{3}-2 \cos \left (\textit {\_Z} \right ) t^{2}+\textit {\_Z}^{2}-4\right ) \]

✓ Mathematica. Time used: 0.244 (sec). Leaf size: 27

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

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

✗ Sympy

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

Timed Out