Internal problem ID [14315]
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: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _exact]
\[ \boxed {\left (3+t \right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (3+t \right ) \cos \left (y+t \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(( (3+t)*cos(t+y(t))+sin(t+y(t)) )+( (3+t)*cos(t+y(t)) )*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = -t +\arcsin \left (\frac {c_{1}}{3+t}\right ) \]
✓ Solution by Mathematica
Time used: 6.0 (sec). Leaf size: 18
DSolve[( (3+t)*Cos[t+y[t]]+Sin[t+y[t]] )+( (3+t)*Cos[t+y[t]] )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -t+\arcsin \left (\frac {c_1}{t+3}\right ) \]