Internal problem ID [15517]
Internal file name [OUTPUT/15518_Friday_May_10_2024_05_47_32_PM_68303959/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: 787.
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 )&=x \left (t \right )^{2}+y \left (t \right )^{2}\\ y^{\prime }\left (t \right )&=2 x \left (t \right ) y \left (t \right ) \end {align*}
Does not currently support non linear system of equations. This is the phase plot of the system.
✓ Solution by Maple
Time used: 0.36 (sec). Leaf size: 65
dsolve([diff(x(t),t)=x(t)^2+y(t)^2,diff(y(t),t)=2*x(t)*y(t)],singsol=all)
\begin{align*} \left [\{y \left (t \right ) = 0\}, \left \{x \left (t \right ) &= \frac {1}{-t +c_{1}}\right \}\right ] \\ \left [\left \{y \left (t \right ) &= \frac {4 c_{1}}{c_{1}^{2} c_{2}^{2}+2 c_{1}^{2} c_{2} t +c_{1}^{2} t^{2}-16}\right \}, \left \{x \left (t \right ) &= \frac {\frac {d}{d t}y \left (t \right )}{2 y \left (t \right )}\right \}\right ] \\ \end{align*}
✓ Solution by Mathematica
Time used: 41.052 (sec). Leaf size: 3516
DSolve[{x'[t]==x[t]^2+y[t]^2,y'[t]==-2*x[t]*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
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