75.1.4 problem 5

Internal problem ID [16667]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 09:16:44 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {x -y} \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 50

dsolve(diff(y(x),x)=sqrt(x-y(x)),y(x), singsol=all)
 

\[ x +\ln \left (-y+x -1\right )+2 \sqrt {x -y}+\ln \left (-1+\sqrt {x -y}\right )-\ln \left (1+\sqrt {x -y}\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 7.400 (sec). Leaf size: 53

DSolve[D[y[x],x]==Sqrt[x-y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -W\left (e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ){}^2-2 W\left (e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )+x-1 \\ y(x)\to x-1 \\ \end{align*}