74.8.31 problem 31

Internal problem ID [16167]
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
Date solved : Tuesday, January 28, 2025 at 08:53:32 AM
CAS classification : [[_homogeneous, `class C`], _exact, _dAlembert]

\begin{align*} \cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.410 (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)
 

\[ y = t -\operatorname {RootOf}\left (\textit {\_Z} -t +\pi -\sin \left (\textit {\_Z} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 59

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

\[ \text {Solve}\left [\int _{\pi }^t-\cos (K[1]-y(t))dK[1]+\int _{\pi }^{y(t)}\left (\cos (t-K[2])-\int _{\pi }^t-\sin (K[1]-K[2])dK[1]-1\right )dK[2]=0,y(t)\right ] \]