77.1.65 problem 85 (page 123)

Internal problem ID [17884]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 85 (page 123)
Date solved : Monday, March 31, 2025 at 04:48:02 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 52

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

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

✓ Mathematica. Time used: 7.581 (sec). Leaf size: 43

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

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

✓ Sympy. Time used: 1.781 (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)
 

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