83.18.16 problem 16

Internal problem ID [19147]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 16
Date solved : Thursday, March 13, 2025 at 01:45:41 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=x^2*diff(y(x),x)^2+x*y(x)*diff(y(x),x)-6*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= c_{1} x^{2} \\ y \left (x \right ) &= \frac {c_{1}}{x^{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 26

ode=x^2*D[y[x],x]^2+x*y[x]*D[y[x],x]-6*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {c_1}{x^3} \\ y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 + x*y(x)*Derivative(y(x), x) - 6*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} x^{2}, \ y{\left (x \right )} = \frac {C_{1}}{x^{3}}\right ] \]