64.6.13 problem 13

Internal problem ID [13284]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 13
Date solved : Wednesday, March 05, 2025 at 09:33:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {x^6+2 x^3+c_1}{\left (x^3+1\right )^2} \\ y(x)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.290 (sec). Leaf size: 15

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

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