Internal problem ID [15523]
Internal file name [OUTPUT/15524_Friday_May_10_2024_05_47_33_PM_58516527/index.tex]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 21. Finding integrable
combinations. Exercises page 219
Problem number: 793.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} x^{\prime }\left (t \right )&=\cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}\\ y^{\prime }\left (t \right )&=-2 \sin \left (x \left (t \right )\right ) \cos \left (x \left (t \right )\right ) \sin \left (y \left (t \right )\right ) \cos \left (y \left (t \right )\right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0] \] Does not currently support non linear system of equations. This is the phase plot of the system.
✗ Solution by Maple
dsolve([diff(x(t),t) = cos(x(t))^2*cos(y(t))^2+sin(x(t))^2*cos(y(t))^2, diff(y(t),t) = -1/2*sin(2*x(t))*sin(2*y(t)), x(0) = 0, y(0) = 0], singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==Cos[x[t]]^2*Cos[y[t]]^2+Sin[x[t]]^2*Cos[y[t]]^2,y'[t]==-1/2*Sin[2*x[t]]*Sin[2*y[t]]},{x[0]==0,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
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