77.1.151 problem 178 (page 265)

Internal problem ID [18041]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 178 (page 265)
Date solved : Tuesday, January 28, 2025 at 08:28:30 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.948 (sec). Leaf size: 29

dsolve([diff(y(x),x)=1-1/z(x),diff(z(x),x)=1/(y(x)-x)],singsol=all)
 

\begin{align*} \{y &= {\mathrm e}^{-c_{1} x} c_{2} +x\} \\ \left \{z \left (x \right ) &= -\frac {1}{y^{\prime }-1}\right \} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 37

DSolve[{D[y[x],x]==1-1/z[x],D[z[x],x]==1/(y[x]-x)},{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*}