Internal problem ID [2356]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 39, page 179
Problem number: 25.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _Clairaut]
\[ \boxed {y-x y^{\prime }+\sqrt {y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 21
dsolve(y(x)=diff(y(x),x)*x-sqrt(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {1}{4 x} \\ y \left (x \right ) &= c_{1} x -\sqrt {c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 23
DSolve[y[x]==y'[x]*x-Sqrt[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\sqrt {c_1} \\ y(x)\to 0 \\ \end{align*}