29.15.35 problem 443

Internal problem ID [5041]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 443
Date solved : Monday, January 27, 2025 at 10:05:21 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 39

dsolve((2+x+y(x))*diff(y(x),x) = 1-x-y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -x -2-\sqrt {-6 c_{1} +6 x +4} \\ y \left (x \right ) &= -x -2+\sqrt {-6 c_{1} +6 x +4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.119 (sec). Leaf size: 43

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

\begin{align*} y(x)\to -x-\sqrt {6 x+4+c_1}-2 \\ y(x)\to -x+\sqrt {6 x+4+c_1}-2 \\ \end{align*}