15.21.9 problem 31

Internal problem ID [3333]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 31
Date solved : Sunday, March 30, 2025 at 01:37:15 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Clairaut]

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

✓ Maple. Time used: 0.065 (sec). Leaf size: 39

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 57

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

\begin{align*} y(x)\to c_1 x-\frac {2}{c_1} \\ y(x)\to \text {Indeterminate} \\ y(x)\to -2 i \sqrt {2} \sqrt {x} \\ y(x)\to 2 i \sqrt {2} \sqrt {x} \\ \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) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out