66.1.38 problem Problem 52

Internal problem ID [13814]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 52
Date solved : Monday, March 31, 2025 at 08:13:46 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(y(x),x)-3*y(x)/x+x^3*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {7 x^{3}}{x^{7}+7 c_1} \]

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 25

ode=D[y[x],x]-3*y[x]/x+x^3*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {7 x^3}{x^7+7 c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.202 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {7 x^{3}}{C_{1} + x^{7}} \]