15.21.10 problem 32

Internal problem ID [3334]
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 : 32
Date solved : Sunday, March 30, 2025 at 01:37:17 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\begin{align*} y &= c_1 \left (x +1\right ) \\ y &= c_1 \left (-1+x \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 (x-1) \\ y(x)\to c_1 (x+1) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.336 (sec). Leaf size: 14

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

\[ \left [ y{\left (x \right )} = C_{1} \left (x - 1\right ), \ y{\left (x \right )} = C_{1} \left (x + 1\right )\right ] \]