Internal problem ID [14294]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {-\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime }=-t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve((t-y(t)*sin(t))+(y(t)^6+cos(t))*diff(y(t),t)=0,y(t), singsol=all)
\[ \frac {t^{2}}{2}+y \left (t \right ) \cos \left (t \right )+\frac {y \left (t \right )^{7}}{7}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 6.808 (sec). Leaf size: 204
DSolve[(t-y[t]*Sin[t])+(y[t]^6+Cos[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,1\right ] \\ y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,2\right ] \\ y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,3\right ] \\ y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,4\right ] \\ y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,5\right ] \\ y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,6\right ] \\ y(t)\to \text {Root}\left [2 \text {$\#$1}^7+14 \text {$\#$1} \cos (t)+7 t^2-14 c_1\&,7\right ] \\ \end{align*}