Internal problem ID [14340]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 58.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +\cos \left (t y\right ) t \right ) y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 27
dsolve((-1+exp(t*y(t))*y(t)+y(t)*cos(t*y(t)))+(1+exp(t*y(t))*t+t*cos(t*y(t)))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {RootOf}\left (t \,{\mathrm e}^{\textit {\_Z}}+t \sin \left (\textit {\_Z} \right )+c_{1} t -t^{2}+\textit {\_Z} \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.475 (sec). Leaf size: 23
DSolve[(-1+Exp[t*y[t]]*y[t]+y[t]*Cos[t*y[t]])+(1+Exp[t*y[t]]*t+t*Cos[t*y[t]])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [e^{t y(t)}+y(t)+\sin (t y(t))-t=c_1,y(t)\right ] \]