60.1.333 problem 334

Internal problem ID [10347]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 334
Date solved : Monday, January 27, 2025 at 07:18:28 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \left (\sqrt {x +y}+1\right ) y^{\prime }+1&=0 \end{align*}

✓ 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)
 

\[ -y-2 \sqrt {x +y}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 39

DSolve[1 + (1 + Sqrt[x + y[x]])*D[y[x],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*}