83.9.4 problem 4

Internal problem ID [21962]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. X at page 57
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:20:09 PM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+y&=y^{2} x^{3} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \frac {1}{\left (-\sin \left (x \right )+x \cos \left (x \right )+c_1 \right ) x} \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {1}{x (-\sin (x)+x \cos (x)+c_1)}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {1}{x \left (C_{1} + x \cos {\left (x \right )} - \sin {\left (x \right )}\right )} \]