7.2.14 problem 16

Internal problem ID [32]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 16
Date solved : Friday, February 07, 2025 at 08:12:19 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 7

dsolve([diff(y(x),x)=sqrt(x-y(x)),y(2) = 1],y(x), singsol=all)
 

\[ y = x -1 \]

✓ Solution by Mathematica

Time used: 0.249 (sec). Leaf size: 8

DSolve[{D[y[x],x]==Sqrt[x-y[x]],{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x-1 \]