75.9.8 problem 227

Internal problem ID [16766]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8.3. The Lagrange and Clairaut equations. Exercises page 72
Problem number : 227
Date solved : Thursday, March 13, 2025 at 08:44:37 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} x {y^{\prime }}^{2}-y y^{\prime }-y^{\prime }+1&=0 \end{align*}

✓ Maple. Time used: 0.159 (sec). Leaf size: 38

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 46

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

\begin{align*} y(x)\to c_1 x-1+\frac {1}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 \sqrt {x}-1 \\ y(x)\to 2 \sqrt {x}-1 \\ \end{align*}

✗ Sympy

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

Timed Out