69.1.4 problem 5

Internal problem ID [17954]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 5
Date solved : Thursday, October 02, 2025 at 02:31:07 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {x -y} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 50

ode:=diff(y(x),x) = (x-y(x))^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ x +\ln \left (-1+x -y\right )+2 \sqrt {x -y}+\ln \left (-1+\sqrt {x -y}\right )-\ln \left (1+\sqrt {x -y}\right )-c_1 = 0 \]

✓ Mathematica. Time used: 4.696 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to -W\left (e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ){}^2-2 W\left (e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )+x-1\\ y(x)&\to x-1 \end{align*}

✓ Sympy. Time used: 0.528 (sec). Leaf size: 27

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

\[ C_{1} + x + 2 \sqrt {x - y{\left (x \right )}} + 2 \log {\left (\sqrt {x - y{\left (x \right )}} - 1 \right )} = 0 \]