64.4.2 problem 2

Internal problem ID [13291]
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
Date solved : Tuesday, January 28, 2025 at 05:16:08 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (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)
 

\[ y = -2+\frac {c_{1}}{\sqrt {x \left (x +2\right )}} \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 92

DSolve[(x*y[x]+2*x+y[x]+2)+(x^2+2*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \exp \left (\int _1^x-\frac {K[1]+1}{K[1]^2+2 K[1]}dK[1]\right ) \left (\int _1^x-\frac {2 \exp \left (-\int _1^{K[2]}-\frac {K[1]+1}{K[1]^2+2 K[1]}dK[1]\right ) (K[2]+1)}{K[2] (K[2]+2)}dK[2]+c_1\right ) \\ y(x)\to -2 \\ \end{align*}