74.6.20 problem 21

Internal problem ID [15972]
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 : Monday, March 31, 2025 at 02:17:18 PM
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*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 13

ode:=exp(t)*sin(y(t))+(1+exp(t)*cos(y(t)))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ {\mathrm e}^{t} \sin \left (y\right )+y+c_1 = 0 \]

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

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

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

✓ Sympy. Time used: 4.215 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((exp(t)*cos(y(t)) + 1)*Derivative(y(t), t) + exp(t)*sin(y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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