71.4.11 problem 11

Internal problem ID [14383]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 06:28:59 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {\frac {y-4}{x}} \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 38

dsolve(diff(y(x),x)=sqrt( (y(x)-4)/x ),y(x), singsol=all)
 

\[ -\ln \left (\frac {-y+4+x}{x}\right )+2 \,\operatorname {arctanh}\left (\sqrt {\frac {y-4}{x}}\right )-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 29

DSolve[D[y[x],x]==Sqrt[ (y[x]-4)/x ],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x+c_1 \sqrt {x}+4+\frac {c_1{}^2}{4} \\ y(x)\to 4 \\ \end{align*}