Internal problem ID [14309]
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: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve((exp(t)*sin(y(t)))+(1+exp(t)*cos(y(t)))*diff(y(t),t)=0,y(t), singsol=all)
\[ {\mathrm e}^{t} \sin \left (y \left (t \right )\right )+y \left (t \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 16
DSolve[(Exp[t]*Sin[y[t]])+(1+Exp[t]*Cos[y[t]])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(t)+e^t \sin (y(t))=c_1,y(t)\right ] \]