Internal problem ID [2288]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x$2)=diff(y(x),x)^2+diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (-c_{1} {\mathrm e}^{x}-c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 1.815 (sec). Leaf size: 31
DSolve[y''[x]==y'[x]^2+y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\log \left (-1+e^{x+c_1}\right ) y(x)\to c_2-i \pi \end{align*}