77.1.150 problem 177 (page 265)

Internal problem ID [17961]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 177 (page 265)
Date solved : Friday, March 14, 2025 at 04:53:30 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y \left (x \right )&=\frac {y \left (x \right )^{2}}{z \left (x \right )}\\ \frac {d}{d x}z \left (x \right )&=\frac {y \left (x \right )}{2} \end{align*}

✓ Maple. Time used: 0.079 (sec). Leaf size: 24

ode:=[diff(y(x),x) = y(x)^2/z(x), diff(z(x),x) = 1/2*y(x)]; 
dsolve(ode);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 45

ode={D[y[x],x]==y[x]^2/z[x],D[z[x],x]==1/2*y[x]}; 
ic={}; 
DSolve[{ode,ic},{y[x],z[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} z(x)\to 2 c_1 \sqrt {\frac {c_1{}^2}{(x+c_1 c_2){}^2}} \\ y(x)\to \frac {4 c_1{}^2}{(x+c_1 c_2){}^2} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(-y(x)**2/z(x) + Derivative(y(x), x),0),Eq(-y(x)/2 + Derivative(z(x), x),0)] 
ics = {} 
dsolve(ode,func=[y(x),z(x)],ics=ics)