Internal problem ID [2357]
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: 26.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-\ln \left (y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(y(x)=diff(y(x),x)*x+ln(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \ln \left (-\frac {1}{x}\right )-1 \\ y \left (x \right ) &= c_{1} x +\ln \left (c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 25
DSolve[y[x]==y'[x]*x+Log[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+\log (c_1) \\ y(x)\to \log \left (-\frac {1}{x}\right )-1 \\ \end{align*}