Internal problem ID [10597]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve((x*y(x)+2*x+y(x)+2)+(x^2+2*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -2+\frac {c_{1}}{\sqrt {x \left (x +2\right )}} \]
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 27
DSolve[(x*y[x]+2*x+y[x]+2)+(x^2+2*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2+\frac {c_1}{\sqrt {x} \sqrt {x+2}} \\ y(x)\to -2 \\ \end{align*}