74.6.20 problem 21

Internal problem ID [16043]
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
Date solved : Tuesday, January 28, 2025 at 08:28:56 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.009 (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)
 

\[ {\mathrm e}^{t} \sin \left (y\right )+y+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 16

DSolve[(Exp[t]*Sin[y[t]])+(1+Exp[t]*Cos[y[t]])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [y(t)+e^t \sin (y(t))=c_1,y(t)\right ] \]