64.4.15 problem 15

Internal problem ID [13304]
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 : 15
Date solved : Tuesday, January 28, 2025 at 05:17:19 AM
CAS classification : [_separable]

\begin{align*} y+2+y \left (x +4\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-3\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.283 (sec). Leaf size: 18

dsolve([(y(x)+2)+(y(x)*(x+4))*diff(y(x),x)=0,y(-3) = -1],y(x), singsol=all)
 

\[ y = -2 \operatorname {LambertW}\left (-\frac {\sqrt {x +4}\, {\mathrm e}^{-\frac {1}{2}}}{2}\right )-2 \]

✓ Solution by Mathematica

Time used: 8.668 (sec). Leaf size: 26

DSolve[{(y[x]+2)+(y[x]*(x+4))*D[y[x],x]==0,{y[-3]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -2 \left (W\left (-\frac {\sqrt {x+4}}{2 \sqrt {e}}\right )+1\right ) \]