Internal problem ID [1693]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {2 t \cos \relax (y)+3 t^{2} y+\left (t^{3}-t^{2} \sin \relax (y)-y\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.219 (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)
\[ y \relax (t ) = \RootOf \left (-2 \textit {\_Z} \,t^{3}-2 \cos \left (\textit {\_Z} \right ) t^{2}+\textit {\_Z}^{2}-4\right ) \]
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 27
DSolve[{2*t*Cos[y[t]]+3*t^2*y[t]+(t^3-t^2*Sin[y[t]]-y[t])*y'[t] == 0,y[0]==2},y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [t^3 y(t)+t^2 \cos (y(t))-\frac {y(t)^2}{2}=-2,y(t)\right ] \]