14.3.6 problem 8

Internal problem ID [2515]
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 : 8
Date solved : Sunday, March 30, 2025 at 12:06:24 AM
CAS classification : [`x=_G(y,y')`]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✗ Maple

ode:=2*t*cos(y(t))+3*t^2*y(t)+(2*y(t)+2*t^2)*diff(y(t),t) = 0; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(2*t*Cos[y[t]]+3*t^2*y[t])+(2*y[t]+2*t^2)*D[y[t],t]==0; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*t**2*y(t) + 2*t*cos(y(t)) + (2*t**2 + 2*y(t))*Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out