Internal problem ID [3863]
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]
\[ \boxed {\left (1+y+y x +y^{2}\right ) y^{\prime }+y=-1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 19
dsolve((1+y(x)+x*y(x)+y(x)^2)*diff(y(x),x)+1+y(x) = 0,y(x), singsol=all)
\[ -c_{1} \left (y \left (x \right )+1\right ) {\mathrm e}^{-y \left (x \right )}+x +y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.143 (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]
\[ \text {Solve}\left [x=-y(x)+c_1 e^{-y(x)} (y(x)+1),y(x)\right ] \]