30.1.5 problem Example, page 33

Internal problem ID [5693]
Book : Differential and integral calculus, vol II By N. Piskunov. 1974
Section : Chapter 1
Problem number : Example, page 33
Date solved : Tuesday, March 04, 2025 at 11:25:49 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.005 (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 \left (x \right ) &= \frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +x^{2}+1}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{x^{2}} c_{1} +x^{2}+1}} \\ \end{align*}

✓ Mathematica. Time used: 7.441 (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: 0.842 (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)
 

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