71.1.151 problem 178 (page 265)

Internal problem ID [19327]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 178 (page 265)
Date solved : Sunday, October 12, 2025 at 05:34:11 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y \left (x \right )&=1-\frac {1}{z \left (x \right )}\\ \frac {d}{d x}z \left (x \right )&=\frac {1}{y \left (x \right )-x} \end{align*}

✓ Maple. Time used: 0.207 (sec). Leaf size: 29

ode:=[diff(y(x),x) = 1-1/z(x), diff(z(x),x) = 1/(y(x)-x)]; 
dsolve(ode);
 

\begin{align*} \{y \left (x \right ) &= {\mathrm e}^{-c_1 x} c_2 +x\} \\ \left \{z \left (x \right ) &= -\frac {1}{\frac {d}{d x}y \left (x \right )-1}\right \} \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 37

ode={D[y[x],x]==1-1/z[x],D[z[x],x]==1/(y[x]-x)}; 
ic={}; 
DSolve[{ode,ic},{y[x],z[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} z(x)&\to \frac {c_1 e^{\frac {x}{c_1}}}{c_2}\\ y(x)&\to x+c_2 e^{-\frac {x}{c_1}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(Derivative(y(x), x) - 1 + 1/z(x),0),Eq(Derivative(z(x), x) - 1/(-x + y(x)),0)] 
ics = {} 
dsolve(ode,func=[y(x),z(x)],ics=ics)
 

NotImplementedError :