Internal problem ID [3355]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 613.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {\left (1+y+y x +y^{2}\right ) y^{\prime }+1+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 36
dsolve((1+y(x)+x*y(x)+y(x)^2)*diff(y(x),x)+1+y(x) = 0,y(x), singsol=all)
\[ x -\left (-\frac {y \relax (x ) {\mathrm e}^{y \relax (x )}}{y \relax (x )+1}+c_{1}\right ) \left ({\mathrm e}^{-y \relax (x )} y \relax (x )+{\mathrm e}^{-y \relax (x )}\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.139 (sec). Leaf size: 23
DSolve[(1+y[x]+x y[x]+y[x]^2)y'[x]+1+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-y(x)+c_1 e^{-y(x)} (y(x)+1),y(x)\right ] \]