74.8.37 problem 37

Internal problem ID [16173]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 37
Date solved : Tuesday, January 28, 2025 at 08:56:09 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

With initial conditions

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

✓ Solution by Maple

Time used: 4.192 (sec). Leaf size: 61

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

\[ y = -{\mathrm e}^{2 \operatorname {RootOf}\left (\textit {\_Z} -x -2 \,{\mathrm e}^{\textit {\_Z}}+3-\ln \left ({\mathrm e}^{\textit {\_Z}} \left ({\mathrm e}^{\textit {\_Z}}-2\right )^{2}\right )\right )}+2 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} -x -2 \,{\mathrm e}^{\textit {\_Z}}+3-\ln \left ({\mathrm e}^{\textit {\_Z}} \left ({\mathrm e}^{\textit {\_Z}}-2\right )^{2}\right )\right )}+x -1 \]

✗ Solution by Mathematica

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

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

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