Internal problem ID [14433]
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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _dAlembert]
\[ \boxed {\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (\pi \right ) = \pi ] \end {align*}
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 19
dsolve([(cos(t-y(t)))+(1-cos(t-y(t)))*diff(y(t),t)=0,y(Pi) = Pi],y(t), singsol=all)
\[ y \left (t \right ) = t -\operatorname {RootOf}\left (\textit {\_Z} -t +\pi -\sin \left (\textit {\_Z} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 21
DSolve[{Cos[t-y[t]]+(1-Cos[t-y[t]])*y'[t]==0,{y[Pi]==Pi}},y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}[-y(t)-\sin (t-y(t))=-\pi ,y(t)] \]