83.21.6 problem 6

Internal problem ID [19179]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (D) at page 57
Problem number : 6
Date solved : Monday, March 31, 2025 at 06:51:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Maple. Time used: 0.077 (sec). Leaf size: 37

ode:=(y(x)-x*diff(y(x),x))*(diff(y(x),x)-1) = diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x +1-2 \sqrt {x} \\ y &= x +1+2 \sqrt {x} \\ y &= c_1 x +\frac {c_1}{c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 42

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

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

✗ Sympy

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

Timed Out