7.2.13 problem 15

Internal problem ID [31]
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 : 15
Date solved : Friday, February 07, 2025 at 08:12:16 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 )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.771 (sec). Leaf size: 49

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

\[ y = \operatorname {RootOf}\left (x +\ln \left (x -\textit {\_Z} -1\right )+2 \sqrt {x -\textit {\_Z}}+\ln \left (\sqrt {x -\textit {\_Z}}-1\right )-\ln \left (1+\sqrt {x -\textit {\_Z}}\right )-2 i \pi -2\right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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