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 : Monday, January 27, 2025 at 05:48:20 AM
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*}

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

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

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

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