29.31.22 problem 921

Internal problem ID [5501]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 921
Date solved : Sunday, March 30, 2025 at 08:25:58 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\begin{align*} y &= \frac {c_1}{a -x} \\ y &= \frac {c_1}{a +x} \\ \end{align*}

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.393 (sec). Leaf size: 14

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

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