23.2.139 problem 142

Internal problem ID [5494]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 142
Date solved : Tuesday, September 30, 2025 at 12:45:33 PM
CAS classification : [_quadrature]

\begin{align*} 4 \left (2-x \right ) {y^{\prime }}^{2}+1&=0 \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 23

ode:=4*(2-x)*diff(y(x),x)^2+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\sqrt {x -2}+c_1 \\ y &= \sqrt {x -2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 31

ode=4(2-x) (D[y[x],x])^2+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {x-2}+c_1\\ y(x)&\to \sqrt {x-2}+c_1 \end{align*}

✓ Sympy. Time used: 0.172 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((8 - 4*x)*Derivative(y(x), x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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