74.6.6 problem 6

Internal problem ID [15958]
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 : 6
Date solved : Monday, March 31, 2025 at 02:16:29 PM
CAS classification : [_exact]

\begin{align*} t -y \sin \left (t \right )+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

ode:=t-y(t)*sin(t)+(y(t)^6+cos(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \frac {t^{2}}{2}+\cos \left (t \right ) y+\frac {y^{7}}{7}+c_1 = 0 \]

✓ Mathematica. Time used: 0.172 (sec). Leaf size: 53

ode=(t-y[t]*Sin[t])+(y[t]^6+Cos[t])*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-y(t) \int _1^t-\sin (K[1])dK[1]+\int _1^t(K[1]-\sin (K[1]) y(t))dK[1]+\frac {y(t)^7}{7}+y(t) \cos (t)=c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t + (y(t)**6 + cos(t))*Derivative(y(t), t) - y(t)*sin(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out