Internal problem ID [15505]
Internal file name [OUTPUT/15506_Friday_May_10_2024_05_47_31_PM_7548041/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 19. Basic concepts and definitions.
Exercises page 199
Problem number: 775.
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 )&=\frac {y \left (t \right )}{x \left (t \right )+y \left (t \right )}+\frac {t}{x \left (t \right )+y \left (t \right )}\\ y^{\prime }\left (t \right )&=\frac {t}{x \left (t \right )+y \left (t \right )}+\frac {x \left (t \right )}{x \left (t \right )+y \left (t \right )} \end {align*}
✓ Solution by Maple
Time used: 1.656 (sec). Leaf size: 3853
dsolve([diff(x(t),t)=(t+y(t))/(y(t)+x(t)),diff(y(t),t)=(t+x(t))/(y(t)+x(t))],singsol=all)
\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x'[t]==(t+y[t])/(y[t]+x[t]),y'[t]==(x[t]+t)/(y[t]+x[t])},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved