Internal problem ID [10240]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1917.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )^{2}-\cos \left (x \left (t \right )\right )\\ y^{\prime }\left (t \right )&=-y \left (t \right ) \sin \left (x \left (t \right )\right ) \end {align*}
✓ Solution by Maple
Time used: 1.25 (sec). Leaf size: 106
dsolve([diff(x(t),t)=y(t)^2-cos(x(t)),diff(y(t),t)=-y(t)*sin(x(t))],singsol=all)
\begin{align*} \left \{x \left (t \right ) &= \operatorname {RootOf}\left (-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{-3 \tan \left (\operatorname {RootOf}\left (-3 \sqrt {-\cos \left (\textit {\_f} \right )^{2}}\, \ln \left (\frac {9 \cos \left (\textit {\_f} \right )^{2} \tan \left (\textit {\_Z} \right )^{2}}{4}+\frac {9 \cos \left (\textit {\_f} \right )^{2}}{4}\right )+c_{1} \sqrt {-\cos \left (\textit {\_f} \right )^{2}}+2 \textit {\_Z} \cos \left (\textit {\_f} \right )\right )\right ) \sqrt {-\cos \left (\textit {\_f} \right )^{2}}+\cos \left (\textit {\_f} \right )}d \textit {\_f} \right )+t +c_{2} \right )\right \} \\ \left \{y \left (t \right ) &= \sqrt {\frac {d}{d t}x \left (t \right )+\cos \left (x \left (t \right )\right )}, y \left (t \right ) &= -\sqrt {\frac {d}{d t}x \left (t \right )+\cos \left (x \left (t \right )\right )}\right \} \\ \end{align*}
✓ Solution by Mathematica
Time used: 124.726 (sec). Leaf size: 3402
DSolve[{x'[t]==y[t]^2-Cos[x[t]],y'[t]==-y[t]*Sin[x[t]]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Too large to display