68.6.26 problem 27

Internal problem ID [17336]
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
Date solved : Thursday, October 02, 2025 at 02:05:22 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

\begin{align*} \left (t +3\right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (t +3\right ) \cos \left (t +y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 16

ode:=(3+t)*cos(t+y(t))+sin(t+y(t))+(3+t)*cos(t+y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -t +\arcsin \left (\frac {c_1}{3+t}\right ) \]

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 104

ode=( (3+t)*Cos[t+y[t]]+Sin[t+y[t]] )+( (3+t)*Cos[t+y[t]] )*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^t(\cos (K[1]+y(t)) K[1]+\cos (K[1]+y(t)) (\tan (K[1]+y(t))+3))dK[1]+\int _1^{y(t)}\left (t \cos (t+K[2])+3 \cos (t+K[2])-\int _1^t(\sec (K[1]+K[2])-K[1] \sin (K[1]+K[2])-\sin (K[1]+K[2]) (\tan (K[1]+K[2])+3))dK[1]\right )dK[2]=c_1,y(t)\right ] \]

✓ Sympy. Time used: 3.445 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t + 3)*cos(t + y(t))*Derivative(y(t), t) + (t + 3)*cos(t + y(t)) + sin(t + y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - t + \operatorname {asin}{\left (\frac {C_{1}}{t + 3} \right )}, \ y{\left (t \right )} = - t - \operatorname {asin}{\left (\frac {C_{1}}{t + 3} \right )} + \pi \right ] \]