63.1.59 problem 78

Internal problem ID [15499]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 78
Date solved : Thursday, October 02, 2025 at 10:18:57 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=1/x^2+3*y(x)^2/x^4 = 2*y(x)/x^3*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {c_1 x -1}\, x \\ y &= -\sqrt {c_1 x -1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 34

ode=1/x^2+ 3*y[x]^2/x^4==2*y[x]/x^3*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.235 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**(-2) - 2*y(x)*Derivative(y(x), x)/x**3 + 3*y(x)**2/x**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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