Internal problem ID [14436]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = \pi ] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 18
dsolve([(y(t)^2)+(2*t*y(t)-2*cos(y(t))*sin(y(t)))*diff(y(t),t)=0,y(0) = Pi],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {RootOf}\left (t \,\textit {\_Z}^{2}+2 \cos \left (\textit {\_Z} \right )-2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 27
DSolve[{(y[t]^2)+(2*t*y[t]-2*Cos[y[t]]*Sin[y[t]])*y'[t]==0,{y[0]==Pi}},y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [t=\frac {1}{2 y(t)^2}-\frac {\cos (2 y(t))}{2 y(t)^2},y(t)\right ] \]