Internal problem ID [8670]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 334.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\left (\sqrt {x +y}+1\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(((x+y(x))^(1/2)+1)*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: 0.097 (sec). Leaf size: 39
DSolve[1 + (1 + Sqrt[x + y[x]])*y'[x]==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*}