64.6.1 problem 1

Internal problem ID [13280]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 1
Date solved : Monday, March 31, 2025 at 07:45:06 AM
CAS classification : [_separable]

\begin{align*} 6 x^{2} y-\left (x^{3}+1\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=6*x^2*y(x)-(x^3+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (x^{3}+1\right )^{2} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 20

ode=6*x^2*y[x]-(x^3+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 \left (x^3+1\right )^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.260 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**2*y(x) - (x**3 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \left (x^{6} + 2 x^{3} + 1\right ) \]