56.17.9 problem Ex 9

Internal problem ID [14190]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 9
Date solved : Thursday, October 02, 2025 at 09:25:47 AM
CAS classification : [_separable]

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

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

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

\begin{align*} y &= c_1 \left (x -2\right ) \\ y &= c_1 \left (x +2\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 26

ode=x^2*(D[y[x],x])^2-2*(x*y[x]+2*D[y[x],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-2)\\ y(x)&\to c_1 (x+2)\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.214 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 - (2*x*y(x) + 4*Derivative(y(x), x))*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} \left (x - 2\right ), \ y{\left (x \right )} = C_{1} \left (x + 2\right )\right ] \]