Internal problem ID [2360]
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: 29.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-{\mathrm e}^{y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(y(x)=diff(y(x),x)*x+exp(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x \left (\ln \left (-x \right )-1\right ) \\ y \left (x \right ) &= c_{1} x +{\mathrm e}^{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 26
DSolve[y[x]==y'[x]*x+Exp[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+e^{c_1} \\ y(x)\to x (\log (-x)-1) \\ \end{align*}