Internal problem ID [9496]
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 }\relax (t )&=y \relax (t )^{2}-\cos \left (x \relax (t )\right )\\ y^{\prime }\relax (t )&=-y \relax (t ) \sin \left (x \relax (t )\right ) \end {align*}
✓ Solution by Maple
Time used: 0.969 (sec). Leaf size: 108
dsolve({diff(x(t),t)=y(t)^2-cos(x(t)),diff(y(t),t)=-y(t)*sin(x(t))},{x(t), y(t)}, singsol=all)
\begin{align*} x \relax (t ) = \RootOf \left (-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{-\tan \left (\RootOf \left (-3 \sqrt {-\left (\cos ^{2}\left (\textit {\_f} \right )\right )}\, \ln \left (\frac {9 \left (\cos ^{2}\left (\textit {\_f} \right )\right )}{4 \cos \left (\textit {\_Z} \right )^{2}}\right )+3 c_{1} \sqrt {-\left (\cos ^{2}\left (\textit {\_f} \right )\right )}+2 \textit {\_Z} \cos \left (\textit {\_f} \right )\right )\right ) \sqrt {-4 \cos \left (2 \textit {\_f} \right )-4-\left (\cos ^{2}\left (\textit {\_f} \right )\right )}+\cos \left (\textit {\_f} \right )}d \textit {\_f} \right )+t +c_{2}\right ) \\ \end{align*} \begin{align*} y \relax (t ) = \sqrt {\frac {d}{d t}x \relax (t )+\cos \left (x \relax (t )\right )} \\ y \relax (t ) = -\sqrt {\frac {d}{d t}x \relax (t )+\cos \left (x \relax (t )\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.563 (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]
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