Internal problem ID [7914]
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]
Solve \begin {gather*} \boxed {\left (\sqrt {x +y}+1\right ) y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 19
dsolve(((x+y(x))^(1/2)+1)*diff(y(x),x)+1 = 0,y(x), singsol=all)
\[ -y \relax (x )-2 \sqrt {x +y \relax (x )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.09 (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*}