77.1.66 problem 86 (page 123)

Internal problem ID [17956]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 86 (page 123)
Date solved : Tuesday, January 28, 2025 at 11:18:17 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {y-x}+1 \end{align*}

✓ Solution by Maple

Time used: 0.087 (sec). Leaf size: 18

dsolve(diff(y(x),x)=sqrt(y(x)-x)+1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.455 (sec). Leaf size: 57

DSolve[D[y[x],x]==Sqrt[y[x]-x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (x^2+(4-2 i c_1) x-c_1{}^2\right ) \\ y(x)\to \frac {1}{4} \left (x^2+(4+2 i c_1) x-c_1{}^2\right ) \\ \end{align*}