74.8.34 problem 34

Internal problem ID [16170]
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
Date solved : Tuesday, January 28, 2025 at 08:55:46 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=\pi \end{align*}

✓ Solution by Maple

Time used: 0.168 (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)
 

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

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 42

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

\[ \text {Solve}\left [t=\frac {\int _0^{y(t)}\sin (2 K[1])dK[1]}{y(t)^2}-\frac {\int _0^{\pi }\sin (2 K[1])dK[1]}{y(t)^2},y(t)\right ] \]