Internal problem ID [3462]
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]
Solve \begin {gather*} \boxed {\left (\sqrt {x +y}+1\right ) y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 19
dsolve((1+sqrt(x+y(x)))*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: 0.085 (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*}