Internal problem ID [3970]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 724.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\left (1+\sqrt {x +y}\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((1+sqrt(x+y(x)))*diff(y(x),x)+1 = 0,y(x), singsol=all)
\[ -y \left (x \right )-2 \sqrt {x +y \left (x \right )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 39
DSolve[(1+Sqrt[x+y[x]])y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \sqrt {x+1+c_1}+2+c_1 y(x)\to 2 \sqrt {x+1+c_1}+2+c_1 \end{align*}