29.25.27 problem 724

Internal problem ID [5314]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 724
Date solved : Monday, January 27, 2025 at 11:08:51 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.025 (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: 0.085 (sec). Leaf size: 39

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