Internal problem ID [12327]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\sqrt {\frac {y-4}{x}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(diff(y(x),x)=sqrt( (y(x)-4)/x ),y(x), singsol=all)
\[ -\ln \left (\frac {x -y \left (x \right )+4}{x}\right )+2 \,\operatorname {arctanh}\left (\sqrt {-\frac {-y \left (x \right )+4}{x}}\right )-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 29
DSolve[y'[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*}