Internal problem ID [14937]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\sqrt {-y+x}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 50
dsolve(diff(y(x),x)=sqrt(x-y(x)),y(x), singsol=all)
\[ x +\ln \left (-y \left (x \right )+x -1\right )+2 \sqrt {-y \left (x \right )+x}+\ln \left (-1+\sqrt {-y \left (x \right )+x}\right )-\ln \left (1+\sqrt {-y \left (x \right )+x}\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 7.657 (sec). Leaf size: 53
DSolve[y'[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*}