Internal problem ID [11638]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y+y \left (4+x \right ) y^{\prime }=-2} \] With initial conditions \begin {align*} [y \left (-3\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 18
dsolve([(y(x)+2)+(y(x)*(x+4))*diff(y(x),x)=0,y(-3) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -2 \operatorname {LambertW}\left (-\frac {\sqrt {x +4}\, {\mathrm e}^{-\frac {1}{2}}}{2}\right )-2 \]
✓ Solution by Mathematica
Time used: 12.779 (sec). Leaf size: 26
DSolve[{(y[x]+2)+(y[x]*(x+4))*y'[x]==0,{y[-3]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 \left (W\left (-\frac {\sqrt {x+4}}{2 \sqrt {e}}\right )+1\right ) \]