88.11.4 problem 4

Internal problem ID [24051]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 54
Problem number : 4
Date solved : Sunday, October 12, 2025 at 05:55:23 AM
CAS classification : system_of_ODEs

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 42

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

\begin{align*} \left \{y \left (x \right ) &= \sqrt {-x^{2}+c_2}, y \left (x \right ) = -\sqrt {-x^{2}+c_2}\right \} \\ \left \{z \left (x \right ) &= \int \frac {2}{y \left (x \right )}d x +c_1\right \} \\ \end{align*}

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 89

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

\begin{align*} y(x)&\to -\sqrt {-x^2+2 c_1}\\ z(x)&\to c_2-2 \arctan \left (\frac {x}{\sqrt {-x^2+2 c_1}}\right )\\ y(x)&\to \sqrt {-x^2+2 c_1}\\ z(x)&\to 2 \arctan \left (\frac {x}{\sqrt {-x^2+2 c_1}}\right )+c_2 \end{align*}

✗ Sympy

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

NotImplementedError :