69.26.6 problem 773

Internal problem ID [18521]
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 : 773
Date solved : Sunday, October 12, 2025 at 05:33:59 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.137 (sec). Leaf size: 61

ode:=[diff(x(t),t) = (t+y(t))/(x(t)+y(t)), diff(y(t),t) = (-t+x(t))/(x(t)+y(t))]; 
dsolve(ode);
 

\begin{align*} [\{x \left (t \right ) = t\}, \{y \left (t \right ) = c_1\}] \\ \left [\left \{x \left (t \right ) &= \frac {c_1 \,t^{2}-c_2 t +1}{c_1 t -c_2}\right \}, \left \{y \left (t \right ) = \frac {-\left (\frac {d}{d t}x \left (t \right )\right ) x \left (t \right )+t}{\frac {d}{d t}x \left (t \right )-1}\right \}\right ] \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq((-t - y(t))/(x(t) + y(t)) + Derivative(x(t), t),0),Eq((t - x(t))/(x(t) + y(t)) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

NotImplementedError :