29.22.7 problem 613

Internal problem ID [5207]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 613
Date solved : Monday, January 27, 2025 at 10:20:57 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} \left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.065 (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)
 

\[ -c_{1} \left (1+y \left (x \right )\right ) {\mathrm e}^{-y \left (x \right )}+x +y \left (x \right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 23

DSolve[(1+y[x]+x y[x]+y[x]^2)D[y[x],x]+1+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=-y(x)+c_1 e^{-y(x)} (y(x)+1),y(x)\right ] \]