77.1.65 problem 85 (page 123)

Internal problem ID [17955]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 85 (page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:15 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.093 (sec). Leaf size: 52

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

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

✓ Solution by Mathematica

Time used: 7.581 (sec). Leaf size: 43

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

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