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 : Monday, January 27, 2025 at 05:56:57 AM
CAS classification : [`x=_G(y,y')`]

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

With initial conditions

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved