15.21.8 problem 30

Internal problem ID [3332]
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 : 30
Date solved : Sunday, March 30, 2025 at 01:37:14 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.070 (sec). Leaf size: 57

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

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

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 73

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

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

✗ Sympy

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

Timed Out