23.2.137 problem 140

Internal problem ID [5492]
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 : 140
Date solved : Tuesday, September 30, 2025 at 12:45:26 PM
CAS classification : [[_homogeneous, `class G`], _rational, _dAlembert]

\begin{align*} 4 x {y^{\prime }}^{2}+4 y y^{\prime }&=1 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 149

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

\begin{align*} \frac {2 x \left (\frac {3 c_1 \left (y-\sqrt {y^{2}+x}\right ) \sqrt {\frac {-y+\sqrt {y^{2}+x}}{x}}}{2}+3 y^{2}-3 y \sqrt {y^{2}+x}+x \right )}{3 \left (y-\sqrt {y^{2}+x}\right )^{2}} &= 0 \\ \frac {2 x \left (-3 c_1 \left (y+\sqrt {y^{2}+x}\right ) \sqrt {\frac {-2 y-2 \sqrt {y^{2}+x}}{x}}+3 y^{2}+3 y \sqrt {y^{2}+x}+x \right )}{3 \left (y+\sqrt {y^{2}+x}\right )^{2}} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 60.149 (sec). Leaf size: 4057

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

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✗ Sympy

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

Timed Out