75.26.8 problem 775

Internal problem ID [17236]
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
Date solved : Tuesday, January 28, 2025 at 08:27:35 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=\frac {t +y \left (t \right )}{x \left (t \right )+y \left (t \right )}\\ \frac {d}{d t}y \left (t \right )&=\frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )} \end{align*}

✓ Solution by Maple

Time used: 8.885 (sec). Leaf size: 1332

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} \\ \left [\{x \left (t \right ) &= \operatorname {RootOf}\left (\textit {\_Z}^{9} c_{1} c_{2} t^{3}-3 \textit {\_Z}^{6} c_{2} t^{3}-1\right )^{3} t +t\}, \left \{y \left (t \right ) = \frac {-x \left (t \right ) \left (\frac {d}{d t}x \left (t \right )\right )+t}{\frac {d}{d t}x \left (t \right )-1}\right \}\right ] \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],t]==(t+y[t])/(y[t]+x[t]),D[y[t],t]==(x[t]+t)/(y[t]+x[t])},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Not solved