74.6.6 problem 6

Internal problem ID [16029]
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 : Tuesday, January 28, 2025 at 08:28:07 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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

\[ \frac {t^{2}}{2}+y \cos \left (t \right )+\frac {y^{7}}{7}+c_{1} = 0 \]

✓ Solution by Mathematica

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

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

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