Internal problem ID [11687]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y=6 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((x^3+1)*diff(y(x),x)+6*x^2*y(x)=6*x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{6}+2 x^{3}+c_{1}}{\left (x^{3}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 29
DSolve[(x^3+1)*y'[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*}