64.6.13 problem 13

Internal problem ID [13363]
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 : Tuesday, January 28, 2025 at 05:32:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[(x^3+1)*D[y[x],x]+6*x^2*y[x]==6*x^2,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*}