83.5.2 problem 1 (b)

Internal problem ID [21937]
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. VI at page 47
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:16:42 PM
CAS classification : [_separable]

\begin{align*} x^{3} y^{\prime }-x^{2} y&=x^{5} y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x^3*diff(y(x),x)-x^2*y(x) = x^5*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {x^{3}}{3}} x \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 23

ode=x^3*D[y[x],x]-x^2*y[x]==x^5*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.169 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5*y(x) + x**3*Derivative(y(x), x) - x**2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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