Internal problem ID [13031]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page
136
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+\sin \left (y\right )^{5}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 190
dsolve(diff(y(t),t)=-sin(y(t))^5,y(t), singsol=all)
\[ y \left (t \right ) = \arctan \left (\frac {2 \,{\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{8 \textit {\_Z}}+8 \,{\mathrm e}^{6 \textit {\_Z}}+64 c_{1} {\mathrm e}^{4 \textit {\_Z}}+24 \textit {\_Z} \,{\mathrm e}^{4 \textit {\_Z}}+64 t \,{\mathrm e}^{4 \textit {\_Z}}-8 \,{\mathrm e}^{2 \textit {\_Z}}-1\right )}}{{\mathrm e}^{2 \operatorname {RootOf}\left ({\mathrm e}^{8 \textit {\_Z}}+8 \,{\mathrm e}^{6 \textit {\_Z}}+64 c_{1} {\mathrm e}^{4 \textit {\_Z}}+24 \textit {\_Z} \,{\mathrm e}^{4 \textit {\_Z}}+64 t \,{\mathrm e}^{4 \textit {\_Z}}-8 \,{\mathrm e}^{2 \textit {\_Z}}-1\right )}+1}, \frac {-{\mathrm e}^{2 \operatorname {RootOf}\left ({\mathrm e}^{8 \textit {\_Z}}+8 \,{\mathrm e}^{6 \textit {\_Z}}+64 c_{1} {\mathrm e}^{4 \textit {\_Z}}+24 \textit {\_Z} \,{\mathrm e}^{4 \textit {\_Z}}+64 t \,{\mathrm e}^{4 \textit {\_Z}}-8 \,{\mathrm e}^{2 \textit {\_Z}}-1\right )}+1}{{\mathrm e}^{2 \operatorname {RootOf}\left ({\mathrm e}^{8 \textit {\_Z}}+8 \,{\mathrm e}^{6 \textit {\_Z}}+64 c_{1} {\mathrm e}^{4 \textit {\_Z}}+24 \textit {\_Z} \,{\mathrm e}^{4 \textit {\_Z}}+64 t \,{\mathrm e}^{4 \textit {\_Z}}-8 \,{\mathrm e}^{2 \textit {\_Z}}-1\right )}+1}\right ) \]
✓ Solution by Mathematica
Time used: 1.165 (sec). Leaf size: 101
DSolve[y'[t]==-Sin[y[t]]^5,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {1}{16} \left (-\frac {1}{64} \csc ^4\left (\frac {\text {$\#$1}}{2}\right )-\frac {3}{32} \csc ^2\left (\frac {\text {$\#$1}}{2}\right )+\frac {1}{64} \sec ^4\left (\frac {\text {$\#$1}}{2}\right )+\frac {3}{32} \sec ^2\left (\frac {\text {$\#$1}}{2}\right )+\frac {3}{8} \log \left (\sin \left (\frac {\text {$\#$1}}{2}\right )\right )-\frac {3}{8} \log \left (\cos \left (\frac {\text {$\#$1}}{2}\right )\right )\right )\&\right ]\left [-\frac {t}{16}+c_1\right ] \\ y(t)\to 0 \\ \end{align*}