63.1.47 problem 66

Internal problem ID [15487]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 66
Date solved : Thursday, October 02, 2025 at 10:18:30 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+y x&=x^{3} y^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 35

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

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_1 +x^{2}+1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_1 +x^{2}+1}} \\ \end{align*}

✓ Mathematica. Time used: 7.124 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to -\frac {1}{\sqrt {x^2+c_1 e^{x^2}+1}}\\ y(x)&\to \frac {1}{\sqrt {x^2+c_1 e^{x^2}+1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.531 (sec). Leaf size: 39

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

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